GIFT  OF 
G.  Fred  Whitworth 


Engineering  Library 
1939 


iih 


ELEMENTARY   LESSONS 

IN 

ELECTRICITY  AND  MAGNETISM 


THE  MACMILLAN  COMPANY 

NEW  YORK   •    BOSTON  •    CHICAGO   •    DALLAS 
ATLANTA  •    SAN   FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON   •   BOMBAY  •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


- 


ELEMENTARY  LESSONS 

IN 

ELECTRICITY  AND  MAGNETISM 


BY 
SILVANUS   P.    THOMPSON 

D.Sc.,  B.A.,  F.R.S.,  F.R.A.S. 

PRINCIPAL  OP  AND  PROFESSOR  OF   PHYSICS    IN   THE   CITY  AND  GUILDS 

OF    LONDON    TECHNICAL   COLLEGE,    FINSBURY 

PROFESSOR    OF   APPLIED   PHYSICS    IN   THE    UNIVERSITY 

OF    LONDON 


SEVENTH   EDITION 
REVISED  AND   ENLARGED 


gotfc 
THE  MACMILLAN   COMPANY 

1917 

All  rights  reserved 


ENGINEERING  LIBRARY 

COPYRIGHT,  1894, 
BY  MACMILLAN  AND  CO. 


Set  up  and  electrotyped.  Published  December,  1894.  Reprinted 
June,  1895;  March,  December,  1896;  October,  1897;  August,  1898; 
August,  1899;  May,  1900;  January,  September,  1901;  March, 
December,  1902;  October,  1903;  April,  1904;  April,  December, 
1905;  July,  1906;  September,  1907;  April,  1908;  August,  1909; 
July,  1910;  January,  1911;  September,  1912;  May,  1914. 


NEW  AND  REVISED  EDITION 

COPYRIGHT,  1915, 
BY  THE  MACMILLAN 


Set  up  and  electrotyptd.     Published  October,  i$IS.     Reprinted 
February,  1916;  September,  1917. 


Nortooob 
J.  8.  Cushing  Co.  —  Berwick  &  Smith  Co. 

Norwood,  Mass.,  U.S.A. 


PREFACE 

FOR  the  purpose  of  the  present  edition  the  entire  work  has 
been  completely  revised,  and  in  many  parts  rewritten.  Prog- 
ress in  the  development  of  the  industrial  applications  of  elec- 
tricity has  been  so  great  in  the  past  decade  as  to  necessitate 
the  remodelling  of  the  latter  half  of  the  book.  A  new  chapter 
has  been  added  on  Wireless  Telegraphy  and  another  on  the 
modern  conception  of  the  Electron. 

The  author  returns  cordial  thanks  to  various  professional 
friends  and  electrical  engineers  who  have  aided  him  with 
information.  He  has  to  thank  Dr.  C.  Chree,  F.R.S.,  of  the 
Kew  Observatory,  for  sundry  magnetic  data,  and  Professor 
L.  A.  Bauer,  of  Washington,  for  material  used  in  preparing 
the  magnetic  map  of  North  America. 

He  is  indebted  for  help  in.  the  revision  to  his  daughter, 
Helen  G-.  Thompson,  B.Sc.,  and  to  his  assistant,  Mr.  Richard 
Gosden,  who  has  been  indefatigable  with  checking  numerical 
calculations,  and  with  proof-reading. 

SILVANUS  P.   THOMPSON. 
JULY,  1916. 


Ri36819 


vii 


Epoch  k 

A.D.I9IO 


Emery  Walker  sc. 

MAGNETIC  CHART  OF  THE  BRITISH  ISLANDS 

SHOWING  THE  LINES  OF  EQUAL  MAGNETIC  DECLINATION  AND 
THOSE  OF  EQUAL  MAGNETIC  DIP 


UrO 


CONTENTS 

PART   FIEST 


CHAPTER  I 
FRICTIONAL  ELECTRICITY 

LESSON 

i/J.  ELECTRIC  ATTRACTION  AND  REPULSION 

•-•  II.  ELECTROSCOPES 

III.  ELECTRIFICATION  BY  INFLUENCE  . 

IV.  CONDUCTION  AND  DISTRIBUTION  OF  ELECTRICITY 
V.  ELECTRIC  MACHINES 

VI.     THE  LEYDEN  JAR  AND  OTHER  CONDENSERS          . 
VII.     OTHER  SOURCES  OF  ELECTRIFICATION  .        . 


PAGE 
1 

15 
22 


44 
62 
70 


CHAPTER  II 

MAGNETISM 

,  VIII.     MAGNETIC  ATTRACTION  AND  REPULSION       ....  81 

IX.     METHODS  OF  MAKING  MAGNETS 93 

«/X.     DISTRIBUTION  OF  MAGNETISM 99 

XL     LAWS  OF  MAGNETIC  FORCE  .         .         .        .         .        .         .  108 

NOTE  ON  WAYS  OF  RECKONING  ANGLES  AND  SOLID  ANGLES  127 

y  XII.     TERRESTRIAL  MAGNETISM 130 


CHAPTER  III 


CURRENT  ELECTRICITY 


XIII.  SIMPLE  VOLTAIC  CELLS 

XIV.  CHEMICAL  ACTIONS  IN  THE  CELL 
XV.     VOLTAIC  CELLS 


144 
164 
159 


Xll 


CONTENTS 


LESSON  PAGE 

XVI.  MAGNETIC  ACTIONS  OF  THE  CURRENT     ....  177 

XVII.     GALVANOMETERS 188 

XVIII.  CURRENTS  PRODUCED  BY  INDUCTION        ....  206 

XIX.     CHEMICAL  ACTIONS  OF  CURRENTS 218 

XX.  PHYSICAL  AND  PHYSIOLOGICAL   EFFECTS.  OF  THE   CUR- 
RENT .  229 


PART   SECOND 

CHAPTER  IV 
ELECTROSTATICS 

XXI.    THEORY  OF  POTENTIAL 

NOTE  ON  FUNDAMENTAL  AND  DERIVED  UNITS 
XXII.     ELECTROMETERS        .         .        . 

XXIII.  DIELECTRIC  CAPACITY,  ETC 

XXIV.  PHENOMENA  OF  DISCHARGE     . 
XXV.     ATMOSPHERIC  ELECTRICITY 


240 
258 
263 
272 
288 
311 


CHAPTER  V 
ELECTROMAGNETICS 

XXVI.     MAGNETIC  POTENTIAL       .... 
^  XXVII.     THE  ELECTROMAGNETIC  SYSTEM  OF  UNITS 
XXVIII.     PROPERTIES  OF  IRON  AND  STEEL     . 

XXIX.       DlAMAGNETISM 

XXX.    THE  MAGNETIC  CIRCUIT  .... 

XXXI.     ELECTROMAGNETS 

XXXII.     ELECTRODYNAMICS    .  ... 


323 
340 
350 
362 
368 
376 
387 


XXXIII. 

XXXIV. 

XXXV. 


CHAPTER  VI 
MEASUREMENTS  OF  CURRENT,  ETC. 

OHM'S  LAW  AND  ITS  CONSEQUENCES 
ELECTRICAL  MEASUREMENTS    .... 
ELECTRIC  ENERGY  AND  MEASUREMENT   . 


400 
417 
433 


CONTENTS 


Xlll 


CHAPTER  VII 
ELECTRIC  PRODUCTION  OF  HEAT 

XXXVI.     HEATING  EFFECT  OF  CURRENTS 
XXXVII.     THERMO-ELECTRIC  CURRENTS 


PAGE 

441 

449 


XXXVIII. 
XXXIX. 


CHAPTER   VIII 
ELECTRIC  LIGHT 


GLOW-LAMPS  . 
ARC  LAMPS    . 


459 
463 


/  XL. 

XLI. 


CHAPTER  IX 

INDUCTANCE 

MUTUAL  INDUCTANCE     . 
SELF-INDUCTANCE  . 


474 

478 


CHAPTER  X 

DYNAMOS,    ALTERNATORS,    AND  TRANSFORMERS 

XLII.     MAGNETO-ELECTRIC    AND    DYNAMO-ELECTRIC    GENER- 
ATORS        486 

XLIII.     ELECTRIC  MOTORS  (CONTINUOUS  CURRENT)          .        .  499 

XLIV.     ALTERNATING  CURRENTS 505 

XLV.     ALTERNATING  CURRENT  GENERATORS  .         .        .        .515 

XLVI.     TRANSFORMERS  AND  CONVERTERS          ....  522 

XL VII.     ALTERNATING-CURRENT  MOTORS    .        .                          ,  630 


CHAPTER  XI 

TRANSMISSION  AND  DISTRIBUTION  OF  POWER 

XLVIII.     ELECTRIC  TRANSMISSION  OF  POWER      .         .        .        .     535 
XLIX.     THE  DISTRIBUTION  OF  POWER  538 


xiv  CONTENTS 


CHAPTER  XII 
ELECTRIC  TRACTION 

LESSON  PAGE 

L.     ELECTRIC  TRAMWAYS  AND  RAILWAYS  646 


CHAPTER  XIII 
ELECTRO-CHEMISTRY 

LI.     ELECTROLYSIS 661 

LII.     ACCUMULATORS .        .         .     665 

LIII.     ELECTRODEPOSITION 668 

CHAPTER  XIV 
TELEGRAPHY 

LIV.  ELECTRIC  TELEGRAPHS        .  573 

LV.  CABLE  TELEGRAPHY 690 

LVI.  MISCELLANEOUS  TELEGRAPHS 694 

LVII.  ELECTRIC  TELEPHONES         .......  697 

CHAPTER  XV 
ELECTRIC  WAVES 

LVIII.     OSCILLATIONS  AND  WAVES  .......     606 

LIX.     THE  ELECTROMAGNETIC  THEORY  OF  LIGHT         .         .        .     617 
LX.    OTHER  RELATIONS  BETWEEN  LIGHT  AND  ELECTRICITY      .    620 

CHAPTER  XVI 

WIRELESS  TELEGRAPHY 

LXI.     RADIOTELEGRAPHY  AND  RADIOTELEPHONY          .        .  627 

CHAPTER  XVII 

ELECTRON  THEORY  OF  ELECTRICITY 
LXII.     ELECTRONS  AND  IONS  .  ,     635 


CONTENTS  XV 

APPENDIX 

PAGE 

APPENDIX  A.    TABLE  OP  ANGLES  AND  SOLID  ANGLES    .        .        .  648 
APPENDIX  B.     ORDER  IN  COUNCIL  LEGALISING  DENOMINATIONS  OF 
STANDARDS  FOR  THE  MEASUREMENT  OF  ELECTRICITY  AS  BOARD 

OF  TRADE  STANDARDS         ........  650 

PROBLEMS  AND  EXERCISES 653 

INDEX 687 

MAGNETIC  MAP  OF  THE  UNITED  STATES  ....       Frontispiece 

MAGNETIC  CHART  OF  THE  BRITISH  ISLANDS     .                 .        .  ix 


ELEMENTARY  LESSONS 

IN 

ELECTRICITY  AND  MAGNETISM 

Part  First 
CHAPTER  I 

FRICTIONAL   ELECTRICITY 

LESSON  I.  —  Electric  Attraction  and  Repulsion 

1.  Electricity.  —  Electricity  is  the  name  given  to  an  in- 
visible agent  known  to  us  only  by  the  effects  which  it  pro- 
duces and  by  various  manifestations  called  electrical.  These 
manifestations,  at  first  obscure  and  even  mysterious,  are 
now  well  understood,  though  little  is  yet  known  of  the  precise 
nature  of  electricity  itself.  Electricity  is  neither  matter  nor 
energy;  yet  it  apparently  can  be  associated  or  combined 
with  matter ;  and  energy  can  be  spent  in  moving  it.  Indeed 
its  great  importance  to  mankind  arises  from  the  circumstance 
that  by  its  means  energy  spent  in  generating  electric  forces 
in  one  part  of  a  system  can  be  made  to  reappear  as  heat  or 
light  or  work  at  some  other  part  of  the  system ;  such  transfer 
of  energy  taking  place  even  to  very  great  distances  at  an  enor- 
mous speed.  Electricity  is  apparently  as  indestructible  as 
matter  or  as  energy.  It  can  neither  be  created  nor  destroyed, 
but  it  can  be  transformed  in  its  relations  to  matter  and  to 
energy,  and  it  can  be  moved  from  one  place  to  another.  In 
many  ways  its  behaviour  resembles  that  of  an  incompres- 
sible liquid ;  in  other  ways  that  of  a  highly  attenuated  and 
weightless  gas.  It  appears  to  exist  distributed  nearly  uni- 

B  1 


2  ELECTRICITY   AND   MAGNETISM          [PT.  i.  2 

fcrmly  ihroughout  all  space.  Many  persons  consider  it  as 
having  to  do  with  the  luminiferous  ether.  There  is  an  inti- 
mate relation  between  the  two.  That  this  must  be  so,  is  a 
necessary  result  of  the  great  discovery  of  Maxwell  —  the 
greatest  scientific  discovery  of  the  nineteenth  century  —  that 
light  itself  is  an  electric  phenomenon,  and  that  the  light- 
waves are  merely  electric,  or,  as  he  put  it,  electromagnetic 
waves.  Electricity  is  now  regarded  as  consisting  of  immense 
numbers  of  excessively  minute  atomic  quantities,  equal 
amongst  themselves,  each  such  atomic  quantity  being  called 
one  electron.  The  modern  doctrine  of  electrons  is  stated  in 
Art.  630,  p.  635. 

2.  The  Science  and  its  Subdivisions.  —  The  name  elec- 
tricity is  also  given  to  that  branch  of  science  which  deals  with 
electric  phenomena  and  theories.  The  phenomena,  and  the 
science  which  deals  with  them,  fall  under  four  heads.  The 
manifestations  of  electricity  when  standing  still  are  different 
from  those  of  electricity  moving  or  flowing  along :  hence 
we  have  to  consider  separately  the  properties  of  (i.)  statical 
charges,  and  those  of  (ii.)  currents.  Further,  electricity  whirl- 
ing round  or  in  circulation  possesses  properties  which  were 
independently  discovered  under  the  name  of  (hi.)  magnetism. 
Lastly,  electricity  when  in  a  state  of  rapid  oscillation  mani- 
fests new  properties  not  possessed  in  any  of  the  previous 
states,  and  causes  the  propagation  of  (iv.)  waves.  These  four 
branches  of  the  science  of  electricity  are,  however,  closely 
connected.  The  object  of  the  present  work  is  to  give  the 
reader  a  general  view  of  the  main  facts  and  their  simple  rela- 
tions to  one  another. 

In  these  first  lessons  we  begin  with  charges  of  electricity, 
their  production  by  friction,  by  influence,  and  by  various 
other  means,  and  shall  study  them  mainly  by  the  manifesta- 
tions of  attraction  and  repulsion  to  which  they  give  rise. 
After  that  we  go  on  to  magnetism  and  currents,  and  the  rela- 
tions between  them.  The  subject  of  electric  waves  is  briefly 
discussed  at  the  end  of  the  book. 


CH.    I.  3] 


ELECTRIC   ATTRACTION 


3.  Electric  Attraction.  —  If  you  take  a  piece  of  sealing- 
wax,  or  of  resin,  or  a  glass  rod,  and  rub  it  upon  a  warm,  dry 
piece  of  flannel  or  silk,  it  will  be  found  to  have  acquired  a 
property  which  it  did  not  previously  possess :  namely,  the 
power  of  attracting  to  itself  such  light  bodies  as  chaff,  or 
dust,  or  bits  of  paper  (Fig.  1).  This  curious  power  was 
originally  discovered  to  be  a  property  of  amber,  or,  as  the 
Greeks  called  it,  fjXtKTpov  (elektron),  which  is  mentioned  by 


FIG.  1.  —  Electric  Attraction  of  Light  Bodies. 

Thales  of  Miletus  (B.C.  600),  and  by  Theophrastus  in  his 
treatise  on  Gems,  as  attracting  light  bodies  when  rubbed. 
Although  an  enormous  number  of  substances  possess  this 
property,  amber  and  jet  were  the  only  two  in  which  its 
existence  had  been  recognized  by  the  ancients,  or  even 
down  to  so  late  a  date  as  the  time  of  Queen  Elizabeth. 
About  the  year  1600,  Dr.  Gilbert  of  Colchester  discovered 
by  experiment  that  not  only  amber  and  jet,  but  a  very 
large  number  of  substances,  such  as  diamond,  sapphire,  rock- 
crystal,  glass,  sulphur,  sealing-wax,  resin,  etc.,  which  he  styled 


4  ELECTRICITY   AND   MAGNETISM          [PT.  i.  4 

electrics,1  possess  the  same  property.  Ever  since  his  time  the 
name  electricity2  has  been  employed  to  denote  the  agent  at 
work  in  producing  these  phenomena.  Gilbert  also  remarked 
that  these  experiments  are  spoiled  by  the  presence  of  moisture. 

4.  Further  Experiments.  —  A  bet- 
ter way  of  observing  the  attracting 
force  is  to  employ  a  small  ball  of 
elder  pith,  or  of  cork,  hung  by  a 
fine  thread  from  a  support,  as  shown 
in  Fig.  2.  A  dry  warm  glass  tube, 
excited  by  rubbing  it  briskly  with  a 
silk  handkerchief,  will  attract  the 
pith-ball  strongly,  showing  that  it 
is  highly  electrified.  The  most  suit- 
able rubber,  if  a  stick  of  sealing- 
wax  is  used,  will  be  found  to  be 
Fia.2.— Attraction  of  Pith-Bali,  flannel,  woollen  cloth,  or,  best  of 

all,  fur.     Boyle  discovered  that  an 

electrified  body  is  itself  attracted  by  one  that  has  not  been 
electrified.  This  may  be  verified  (see  Fig.  3)  by  rubbing  a 
stick  of  sealing-wax,  or  a  glass  rod,  and  hanging  it  in  a  wire 
loop  at  the  end  of  a  silk  thread.  If,  then,  the  hand  be  held 
out  towards  the  suspended  electrified  body,  the  latter  will 
turn  round  and  approach  the  hand.  So,  again,  a  piece  of 
silk  ribbon,  if  rubbed  with  warm  indiarubber,  or  even  if 
drawn  between  two  pieces  of  warm  flannel,  and  then  hung 
up  by  one  end,  will  be  found  to  be  attracted  by  objects  pre- 
sented to  it.  If  held  near  the  wall  of  the  room  it  will  fly 
to  it  and  stick  to  it. 

With  proper  precautions  it  can  be  shown  that  both  the 
rubber  and  the  thing  rubbed  are  in  an  electrified  state,  for 

1  "  Electrica :    quae  attrahunt  eadem  ratione  ut  electrum  "  (Gilbert). 

2  The  first  work  in  which   this  term  was  used  is  that  of  Dr.  Thomas 
Browne,  Enquiries  into  Vulgar  and  Common  Errors,  published  in  London, 
1646  :   the  oldest  book  devoted  to  electricity  is  Robert  Boyle's  Experiments 
and  Notes  about  the  Mechanical  Origine  or  Production  of  Electricity,  printed  at 
Oxford,  1675. 


CH.  i.  5]          ELECTRIFICATION   BY   FRICTION 


FIG.  3.  —  Rubbed  Glass  Rod  attracted  by 
the  Hand. 


both  will  attract  light  bodies  ;  but  to  show  this,  care  must  be 
taken  not  to  handle  the  rubber  too  much.  Thus,  if  it  is  de- 
sired to  show  that  when  a 
piece  of  fur  is  rubbed  upon 
sealing-wax,  the  fur  becomes 
also  electrified,  it  is  better  not 
to  take  the  fur  in  the  hand, 
but  to  cement  it  to  the  end  of 
a  glass  rod  as  a  handle.  The 
reason  of  this  precaution  will 
be  explained  toward  the  close 
of  this  lesson,  and  more  fully 
in  Lesson  IV. 

A   large    number    of    sub- 
stances, including  iron,  gold, 

brass,  indeed  all  the  metals,  and  stony  substances  such  as  slate 
and  marble,  and  ordinary  woods,  when  held  in  the  hand  and 
rubbed,  exhibit  no  sign  of  electrification  —  that  is  to  say,  do 
not  attract  light  bodies  as  rubbed  amber  and  rubbed  glass  do. 
Such  bodies  were,  on  that  account,  formerly  termed  non- 
electrics;  but  the  term  is  erroneous,  for  if  they  are  mounted 
on  glass  handles  and  then  rubbed  with  silk  or  fur,  they  be- 
have as  electrics. 

5.  Electric  Repulsion.  —  When  experimenting,  as  in  Fig.  1, 
with  a  rubbed  glass  rod  and  bits  of  chopped  paper,  or  straw, 
or  bran,  it  will  be  noticed  that  these  little  bits  are  first  at- 
tracted and  fly  up  towards  the  excited  rod  ;  but  that,  having 
touched  it,  they  arc  speedily  repelled  and  fly  back  to  the  table. 
To  show  this  repulsion  better,  let  a  small  piece  of  feather  or 
down  be  hung  by  a  silk  thread  to  a  support,  and  let  an  elec- 
trified glass  rod  be  held  near  it.  It  will  dart  towards  the 
rod  and  stick  to  it,  and  a  moment  later  will  dart  away  from 
it,  repelled  by  an  invisible  force  (Fig.  4),  nor  will  it  again 
dart  towards  the  rod.  If  the  experiment  be  repeated  with 
another  feather,  and  a  stick  of  sealing-wax  rubbed  on  flannel, 
the  same  effects  will  occur.  But  if  now  the  hand  be  held 


6 


ELECTRICITY   AND   MAGNETISM          [PT.  i.  6 


FIG.  4.  —  Repulsion  of  Feather. 


towards  the  feather,  it  will  rush  toward  the  hand,  as  the 
rubbed  body  (in  Fig.  3)  did.  This  proves  that  the  feather, 

though  it  has  not  itself  been  rubbed, 
possesses  the  property  originally 
imparted  to  the  rod  by  rubbing  it. 
In  fact,  it  has  become  electrified,  by 
having  touched  an  electrified  body 
which  has  given  part  of  its  elec- 
tricity to  it.  It  would  appear  then 
that  two  bodies  electrified  with  the 
same  electrification  repel  one  an- 
other. This  may  be  confirmed  by 
a  further  experiment.  A  rubbed 
glass  rod,  hung  up  as  in  Fig.  3,  is 
repelled  by  a  similar  rubbed  glass 
rod ;  while  a  rubbed  stick  of  seal- 
ing-wax is  repelled  by  a  second 

rubbed  stick  of  sealing-wax.  Another  way  of  showing 
the  repulsion  between  two  similarly  electrified  bodies  is 
to  hang  a  couple  of  small  pith-balls,  by  thin  linen  threads, 
to  a  glass  support,  as  in  Fig.  5,  and  then  touch  them 
both  with  a  rubbed  glass  rod.  They  repel  one  another 
and  fly  apart,  instead  of  hanging  down  side  by  side; 
while  the  near  presence  of  the  glass  rod  will  make  them 
open  out  still  wider,  for  now  it  repels  them  both.  The 
self -repulsion  of  the  parts  of  an  electrified  body  is  beautifully 
illustrated  by  the  experiment  of  electrifying  a  soap-bubble, 
which  expands  when  electrified. 

6.  Two  Kinds  of  Electrification.  —  Electrified  bodies  do 
not,  however,  always  repel  one  another.  The  feather  which 
(see  Fig.  4)  has  been  touched  by  a  rubbed  glass  rod,  and  which 
in  consequence  is  repelled  from  the  rubbed  glass,  will  be 
attracted  if  a  stick  of  rubbed  sealing-wax  be  presented  to  it ; 
and  conversely,  if  the  feather  has  been  first  electrified  by 
touching  it  with  the  rubbed  sealing-wax,  it  will  be  attracted 
to  a  rubbed  glass  rod,  though  repelled  by  the  rubbed  wax. 


CH.    I.  6] 


OPPOSITE   ELECTRIC   STATES 


FIG.  5.  —  Repulsion  between  Pith-Balls. 


So,  again,  a  rubbed  glass  rod  suspended  as  in  Fig.  3  will  be 
attracted  by  a  rubbed  piece  of  sealing-wax,  or  resin,  or  am- 
ber, though  repelled  by  a 
rubbed  piece  of  glass.  The 
two  pith-balls  touched  (as  in 
Fig.  5)  with  a  rubbed  glass 
rod  fly  from  one  another  by 
repulsion,  and,  as  we  have 
seen,  fly  wider  asunder  when 
the  excited  glass  rod  is  held 
near  them;  yet  they  fall 
nearer  together  when  a 
rubbed  piece  of  sealing-wax 
is  held  under  them,  being 

attracted  by  it.  Symmer  first  observed  such  phenomena 
as  these,  and  they  were  independently  discovered  by  Du 
Fay,  who  suggested,  in  explanation  of  them,  that  there 
were  two  different  kinds  of  electricity  which  attracted  one 
another,  while  each  repelled  itself.  The  electricity  produced 
on  glass  by  rubbing  it  with  silk  he  called  vitreous  electricity, 
supposing,  though  erroneously,  that  glass  could  yield  no 
other  kind ;  and  the  electricity  excited  in  such  substances 
as  sealing-wax,  resin,  shellac,  indiarubber,  and  amber,  by 
rubbing  them  on  wool  or  flannel,  he  termed  resinous  electric- 
ity. The  kind  of  electricity  produced  is,  however,  found 
to  depend  not  only  on  the  thing  rubbed  but  on  the  rubber 
also ;  for  glass  yields  "  resinous  "  electricity  when  rubbed 
with  a  cat's  skin,  and  resin  yields  "  vitreous  "  electricity 
if  rubbed  with  a  soft  amalgam  of  tin  and  mercury  spread 
on  leather.  Hence  these  names  have  been  abandoned  in 
favour  of  the  more  appropriate  terms  introduced  by  Franklin, 
who  called  the  electricity  excited  upon  glass  by  rubbing  it 
with  silk,  positive  electricity,  and  that  produced  on  resinous 
bodies  by  friction  with  wool  or  fur,  negative  electricity.  The 
observations  of  Symmer  and  Du  Fay  "may  therefore  be  stated 
as  follows:  —  Two  positively  electrified  bodies  apparently 


8  ELECTRICITY   AND   MAGNETISM     [PT.  i.  7,  8 

repel  one  another :  two  negatively  electrified  bodies  appar- 
ently repel  one  another  :  but  a  positively  electrified  body  and 
a  negatively  electrified  body  apparently  attract  one  another. 
It  is  now  known  that  these  effects  which  appear  like  a  repul- 
sion' and  an  attraction  between  bodies  at  a  distance  from 
one  another,  are  really  due  to  actions  going  on  in  the  medium. 
between  them.  The  positive  charge  does  not  really  attract 
the  negative  charge  that  is  near  it ;  but  both  are  urged  toward 
one  another  by  stresses  in  the  medium  in  the  intervening 
space. 

7.  Simultaneous  Production  of  both  Electrical  States.  - 
Neither  kind   of  electrification    is    produced   alone ;    there 
is  always  an  equal  quantity  of  both  kinds  produced ;    one 
kind  appearing  on  the  thing  rubbed  and  an  equal  amount 
of  the  other  kind  on  the  rubber.     It  is  possible  in  certain 
cases  to  give  clear  proof  that  these  amounts  are  equal.     For  it 
is  found  that  if  both  the  electricity  of  the  rubber  and  the 
electricity  of  the  thing  rubbed  be  imparted  to  a  third  body, 
that  third  body  will  show  no  electrification  at  all,  the  two 
equal  and  opposite  electrifications  having  exactly  neutralized 
each  other.     A  simple  experiment  consists  in  rubbing  together 
two  disks,  one  of  sealing-wax,  and  the  other  of  wood  covered 
with  flannel,  both  being  held  by  handles  of  glass  or  ebonite. 
To  test  them  an  insulated  pot  and  an  electroscope  are  required 
as  in  Fig.  28.     If,  after  being  rubbed  together,  either  disk 
be  inserted  in  the  pot  the  leaves  of  the  electroscope  will  di- 
verge ;    but  if  both  are  inserted  at  the  same  time  the  leaves 
do  not  diverge,  showing  that  the  two  charges  on  the  disks  are 
equal  and  of  opposite  sign. 

In  the  following  list  the  bodies  are  arranged  in  such  an 
order  that  if  any  two  be  rubbed  together  the  one  which 
stands  earlier  in  the  series  becomes  positively  electrified,  and 
the  one  that  stands  later  negatively  electrified  :  —  Fur,  wool, 
ivory,  glass,  silk,  metals,  sulphur,  indiarubber,  guttapercha,  col- 
lodion or  celluloid. 

8.  Theories  of  Electricity.  —  Several  theories  have  been 


CH.  i.  8]  THEORIES   OF   ELECTRICITY  9 

advanced  to  account  for  these  phenomena.  Symmer  proposed 
a  "  two-fluid  "  theory,  according  to  which  there  are  two  im- 
ponderable electric  fluids  of  opposite  kinds,  which  neutralize 
one  another  when  they  combine,  and  which  exist  combined 
in  equal  quantities  in  all  bodies  until  their  condition  is  dis- 
turbed by  friction  or  otherwise.  A  modification  of  this  theory 
was  made  by  Franklin,  who  proposed  instead  a  "  one-fluid  " 
theory,  according  to  which  there  is  a  single  electric  fluid  dis- 
tributed usually  uniformly  in  all  bodies,  but  which,  when 
they  are  subjected  to  friction,  distributes  itself  unequally  be- 
tween the  rubber  and  the  thing  rubbed,  one  having  more  of  the 
fluid,  the  other  less,  than  the  average.  Hence  the  terms  posi- 
tive and  negative,  which  are  still  retained.  That  body  which  is 
supposed  to  have  an  excess  being  said  to  be  charged  with  posi- 
tive electricity  (usually  denoted  by  the  plus  sign  +  ),  while 
that  which  is  supposed  to  have  less  is  said  to  be  charged 
with  negative  electricity  (and  is  denoted  by  the  minus  sign 
— ).  These  terms  are,  however,  purely  arbitrary,  for  in  the 
present  state  of  science  we  are  not  certain  which  of  these  two 
states  really  means  more  and  which  means  less ;  but  appar- 
ently it  follows  from  recent  researches  (see  Art.  630)  that  the 
kind  of  electrification  called  resinous  or  negative  is  that  in 
which  there  is  an  excess  of  electrons.  In  many  ways  electric- 
ity behaves  as  a  weightless  substance  as  incompressible  as 
any  material  liquid.  It  is,  however,  quite  certain  that  elec- 
tricity is  not  a  material  fluid,  whatever  else  it  may  be.  For 
while  it  resembles  a  fluid  in  its  property  of  apparently  flowing 
from  one  point  to  another,  it  differs  from  every  known  fluid  in 
almost  every  other  respect.  The  electrons,  or  atoms  of  elec- 
tricity, repel  one  another  and  thus  differ  fundamentally  from 
the  particles  of  matter,  which  are  mutually  attractive.  It  is, 
moreover,  quite  impossible  to  conceive  of  two  fluids  whose 
properties  should  in  every  respect  be  the  precise  opposites 
of  one  another.  For  these  reasons  it  is  misleading  to  speak  of 
an  electric  fluid  or  fluids,  however  convenient  the  term  may 
seem  to  be.  In  metals  and  other  good  conductors  electricity 


10  ELECTRICITY   AND   MAGNETISM          [PT.  i.  9 

can  apparently  move  and  flow  quite  easily  in  currents.  In 
transparent  solids  such  as  glass  and  resin,  and  in  many  trans- 
parent liquids  such  as  oils,  and  in  gases  such  as  the  air  (if 
still,  and  not  rarefied),  electricity  apparently  cannot  flow. 
Even  a  vacuum  appears  to  be  a  non-conductor.  In  the  case 
of  all  non-conductors  (except  when  they  are  disrupted  or 
pierced  by  a  discharge)  electricity  can  only  be  moved  by  an 
action  known  as  displacement  (see  Art.  58). 

It  appears  then  that  in  metals  electricity  can  easily  pass 
from  molecule  to  molecule,  and  from  atom  to  atom;  but 
in  the  case  of  non-conductors  the  electricity  is  in  some  way 
stuck  to  the  molecules,  or  associated  with  them.  Some 
electricians,  notably  Faraday,  have  regarded  the  electrical 
states  as  being  the  result  of  certain  peculiar  conditions  of  the 
molecules  of  the  surfaces  that  have  been  rubbed.  Another 
view  is  to  regard  the  state  of  electrification  as  related  to  the 
ether  (the  highly-attenuated  medium  which  fills  all  space, 
and  is  the  vehicle  by  which  light  is  transmitted),  which  is 
known  to  be  associated  with  the  atoms  of  matter.  Some 
indeed  hold  that  the  ether  itself  is  electricity ;  and  that  the 
two  states  of  positive  and  negative  electrification  are  due  to 
displacement  of  the  ether  at  the  surfaces  of  the  charged 
bodies.  In  these  lessons  we  shall  avoid  as  far  as  possible  all 
theories,  and  shall  be  content  to  use  the  term  electricity. 

9.  Charge.  —  The  quantity  of  electrification  of  either 
kind  produced  by  friction  or  other  means  upon  the  surface 
of  a  body  is  spoken  of  as  a  charge,  and  a  body  when  electrified 
is  said  to  be  charged.  It  is  clear  that  there  may  be  charges  of 
different  amounts  and  they  may  be  of  either  kind.  The  word 
charge  implies  that  the  electricity  is  in  the  static  condition, 
that  is,  is'aZ  rest  on  the  surface  of  the  body.  When  the  charge 
of  electricity  is  removed  from  a  charged  body,  the  body  is 
said  to  be  discharged.  A  charge  given  to  a  conductor,  such 
as  a  piece  of  metal,  will  not  be  retained  by  it,  unless  the  con- 
ductor be  insulated,  that  is,  held  on  some  non-conducting 
support.  Conductors  of  electricity  are  instantaneously 


CH.  1.10,11]  MODES  OF  SHOWING  ELECTRIFICATION    11 

discharged  if  touched  by  the  hand  or  by  any  conductor  in 
contact  with  the  ground,  the  charge  thus  finding  a  means  of 
escaping  to  earth  or  to  surrounding  walls.  A  charged  non- 
conductor such  as  a  rubbed  rod  of  glass  or  ebonite  may  be 
readily  and  completely  dis-electrified  by  passing  it  through, 
or  even  holding  it  near  to,  a  flame.  (See  also  Art.  334, 
p.  292.) 

Electricity  may  either  reside  upon  the  surface  of  bodies 
as  a  charge,  or  flow  through  their  substance  as  a  current. 
That  branch  of  the  science  which  treats  of  the  laws  of  the 
charges,  that  is  to  say,  of  electricity  at  rest  upon  the  surface 
of  bodies,  is  termed  electrostatics,  and  is  dealt  with  in  Chap- 
ter IV.  The  branch  of  the  subject  which  treats  of  the  flow 
of  electricity  in  currents  is  dealt  with  in  Chapter  III,  and 
other  later  portions  of  this  book. 

10.  Modes     of     representing     Electrification.  —  Several 
modes  are  used  to  represent  the  electrification  of  surfaces. 
In  Figs.  6,  7,  and  8  are  represented 

two  disks  —  A  covered  with  woollen   A    j5 

cloth,  B  of  some  resinous  body  - 

which   have  been  rubbed  together 

so  that   A   has   become  positively, 

B   negatively   electrified.     In   Fig. 

6    the    surfaces    are    marked   with    FlG' 6'        FlG<  7'      .FlG-8' 

T         /    ,   \  i         •  /       \  Modes  of  Representation  of 

PLUS  (+)   and  minus  (—)  Signs.       In  Electrification. 

Fig.  7  dotted  lines  are  drawn  just 

outside  the  positively  electrified  surface  and  just  within 
the  negatively  electrified  surface,  as  though  one  had  a 
surplus  and  the  other  a  deficit  of  electricity.  In  Fig.  8 
lines  are  drawn  across  the  intervening  space  from  the  posi- 
tively electrified  surface  to  the  opposite  negative  charge. 
The  advantages  of  this  last  mode  are  explained  in  Art.  14. 

11.  Conductors    and    Insulators.  —  The   term    "  conduc- 
tors/' used  above,  is  applied  to  those  bodies  which  readily 
allow  electricity  to  flow  through  them.     Broadly  speaking, 
bodies  may  be  divided  into  two  classes  —  those  which  con- 


12  ELECTRICITY   AND   MAGNETISM      [PT.  i.  12,  13 

duct  and  those  which  do  not  ;  though  very  many  substances 
are  partial  conductors,  and  cannot  well  be  classed  in  either 
category.  All  the  metals  conduct  well ;  the  human  body 
conducts,  and  so  does  water.  On  the  other  hand  glass,  porce- 
lain, sealing-wax,  silk,  shellac,  guttapercha,  indiarubber,  resin, 
oils  and  fatty  substances  generally,  and  the  air,  are  non-con- 
ductors. On  this  account  these  substances  are  used  to  make 
supports  and  handles  for  electrical  apparatus  where  it  is  impor- 
tant that  the  electricity  should  not  leak  away ;  hence  they  are 
sometimes  called  insulators  (see  Arts.  30  and  437).  Faraday 
termed  them  dielectrics,  Art.  25.  We  have  remarked  above 
that  the  name  of  non-electrics  was  given  to  those  substances 
which,  like  the  metals,  yield  no  sign  of  electrification  when 
held  in  the  hand  and  rubbed.  We  now  know  the  reason  why 
they  show  no  electrification ;  for,  being  good  conductors,  the 
electrification  flows  away  as  fast  as  it  is  generated.  The 
observation  of  Gilbert  that  electrical  experiments  fail  in  damp 
weather  is  also  explained  by  the  knowledge  that  water  is  a 
conductor,  the  film  of  moisture  on  the  surface  of  damp  bodies 
causing  the  charges  produced  by  friction  to  leak  away  as  fast 
as  they  are  generated. 

12.  Other  Electrical  Effects.  —  The  production  of  elec- 
tricity by  friction  is  attested  by  other  effects  than  those  of 
attraction  and  repulsion,  which  hitherto  we  have  assumed  to 
be  the  test  of  the  presence  of  electricity.     Otto  von  Guericke 
first  observed  that  sparks  and  flashes  of  light  could  be  ob- 
tained from  highly  electrified  bodies  at  the  moment  when  they 
were  discharged.     Such  sparks  are  usually  accompanied  by  a 
snapping  sound,   suggesting  on  a  small  scale  the  thunder 
accompanying  the  lightning  flash,  as  was  indeed  remarked  by 
Newton  and  other  early  observers.     Pale  flashes  of  light  are 
also  produced  by  the  discharge  of  electricity  through  tubes 
partially  exhausted  of  air  by  the  air-pump.     Other  effects 
will  be  noticed  in  due  course. 

13.  Sources   of   Electrification.  —  But  friction   is   by   no 
means  the  only  source  of  electrification.     The  other  sources, 


CH.  i.  13]        SOURCES   OF   ELECTRIFICATION  13 

percussion,  compression,  heat,  chemical  action,  physiological 
action,  contact  of  metals,  etc.,  will  be  treated  of  in 
Lesson  VII.  We  will  simply  remark  here  that  friction 
between  two  different  substances  always  produces  electrical 
separation,  no  matter  what  the  substances  may  be.  Sym- 
mer  observed  the  production  of  electrification  when  a  silk 
stocking  was  drawn  over  a  woollen  one,  though  woollen 
rubbed  upon  woollen,  or  silk  rubbed  upon  silk,  produces  no 
electrical  effect.  If,  however,  a  piece  of  rough  glass  be  rubbed 
on  a  piece  of  smooth  glass,  electrification  is  observed ;  and 
indeed  the  conditions  of  the  surface  play  a  very  important 
part  in  the  production  of  electrification  by  friction.  In 
general,  of  two  bodies  thus  rubbed  together,  that  one  becomes 
negatively  electrical  whose  particles  are  the  more  easily  re- 
moved by  friction.  Differences  of  temperature  also  affect 
the  electrical  conditions  of  bodies,  a  warm  body  being  usually 
negative  when  rubbed  on  a  cold  piece  of  the  same  substance. 
The  quantity  of  electrification  produced  is,  however,  not 
proportional  to  the  amount  of  the  actual  work  expended  on 
mechanical  friction  ;  hence  it  appears  doubtful  whether  fric- 
tion is  truly  the  cause  of  the  electrification.  When  the  sur- 
faces of  two  different  substances  are  brought  into  intimate 
contact  something  certainly  happens,  which  has  the  result 
that  when  they  are  drawn  apart  they  are  found  (provided 
at  least  one  of  them  is  a  non-conductor)  to  have  acquired 
opposite  charges  of  electrification ;  one  surface  having  ap- 
parently taken  some  electricity  from  the  other.  But  these 
opposite  charges  attract  one  another  and  cannot  be  drawn 
apart  without  there  being  mechanical  work  done  upon  the 
system.  The  work  thus  spent  is  stored  up  in  the  act  of  sepa- 
rating the  charged  surfaces ;  and  as  long  as  the  charges  re- 
main separated  they  constitute  a  store  of  potential  energy. 
The  so-called  frictional  electric  machines  are  therefore 
machines  for  bringing  dissimilar  substances  into  intimate 
contact,  and  then  drawing  apart  the  particles  that  have 
touched  one  another  and  have  acquired  electric  charges. 


14  ELECTRICITY   AND   MAGNETISM        [PT.  i.  14 

If  the  two  bodies  that  are  rubbed  together  are  both  good 
conductors,  they  will  not  become  strongly  electrified,  even 
if  held  on  insulating  handles.  It  is  quite  likely,  however, 
that  the  heat  produced  by  friction,  as  in  the  bearings  of  ma- 
chinery, is  due  to  electric  -currents  generated 
where  the  surfaces  meet  and  slip. 

14.  Electric  Field.  —  Whenever  two  oppo- 
sitely charged  surfaces  are  placed  near  one  an- 
other they  tend  to  move  together,  and  the 
ptoreFieid.  ex~  space  between  them  is  found  to  be  in  a  pe- 
culiar state  of  stress,  as  though  the  medium 
in  between  had  been  stretched.  To  explore  the  space  be- 
tween two  bodies  one  of  which  has  been  positively  and 
the  other  negatively  electrified,  we  may  use  a  light 
pointer  (Fig.  9)  made  of  a  small  piece  of  very  thin  paper 
pierced  with  a  hole  through  which  passes  a  long  thread  of 
glass.  It  will  be  found  that  this  pointer  'tends  to  point 
across  from  the  positively  electrified  surface  to  the  negatively 
electrified  surface,  along  invisible  lines  of  electric  force.  The 
space  so  filled  with  electric  lines  of  force  is  called  an  electric 
field.  In  Fig.  8,  A  and  B  represent  two  bodies  the  surfaces 
of  which  have  been  electrified,  the  one 
positively,  the  other  negatively.  In  the 
field  between  them  the  electric  lines  pass 
across  almost  straight,  except  near  the 
edges,  where  they  are  curved.  Electric 
lines  of  force  start  from  a  positively 
charged  surface  at  one  end,  and  end  on 
a  negatively  charged  surface  at  the  other 
end.  They  never  meet  or  cross  one  ^ 

J  FIG.    10.  —  Electric    Forces 

another.     Their  direction  indicates  that      around  Charged  Bail. 
of  the  resultant  electric  force  at  every 
point  through  which  they  pass.     The  stress  in  the  medium 
thus  mapped  out  by  the  lines  of  force  acts  as  a  tension 
along  them,  as  though  they  tended  to  shorten  themselves. 
In  fact  in  Fig.  8  the  tension  in  the  medium  draws  the 


CH.  i.  15-17]       GOLD-LEAF  ELECTROSCOPE 


15 


two  surfaces  together.  There  is  also  a  pressure  in  the 
medium  at  right  angles  to  the  lines,  tending  to  widen  the 
distance  between  them.  Fig.  10  represents  a  ball  which 
has  been  positively  electrified,  and  placed  at  a  distance  from 
other  objects ;  the  lines  in  the  field  being  simply  radial. 
Curved  lines  of  force  are  found  in  the  electric  fields  between 
two  electrified  sources  as  in  Fig.  15,  p.  22. 


FIG.  11.  —  Needle  Electroscope. 


LESSON  II.  —  Electroscopes 

16.  Simple  Electroscopes.  —  An  instrument  for  detecting 
whether  a  body  is  electrified  or  not,  and  whether  the  elec- 
trification is  positive  or 
negative,  is  termed  an 
Electroscope.  The 
feather  which  was  at- 
tracted or  repelled,  and 
the  two  pith-balls  which 
flew  apart  when  elec- 
trified, as  we  found  in  Lesson  I.,  are  in  reality  simple 
electroscopes.  There  are,  however,  a  number  of  pieces  of 
apparatus  better  adapted  for  this  patricular  purpose,  some 
of  which  we  will  describe. 

16.  Needle  Electroscope.  —  The  earliest  electroscope  was 
that  devised  by  Dr.  Gilbert,  and,  as  is  shown  in  Fig.  11,  con- 
sists of  a  stiff  strip  balanced  lightly  upon  a  sharp  point.     A 
thin  strip  of  brass  or  wood,  a  straw,  or  even  a  goose  quill, 
balanced   upon  a   sewing    needle,  will    serve   equally  well. 
When  an  electrified  body  is  held  near  the  electroscope  it  is 
attracted  and  turned  round,  and  will  thus  indicate  the  pres- 
ence of  electric  charges  far  too  feeble  to  attract  bits  of  paper 
from  a  table. 

17.  Gold-Leaf    Electroscope.  —  A    still    more    sensitive 
instrument  is  the  Gold-Leaf  Electroscope  invented  by  Ben- 
net,  and  shown  in  Fig.  12.     We  have  seen  how  two  pith- 
balls  when  similarly  electrified  repel  one  another  and  stand 


16 


ELECTRICITY   AND   MAGNETISM        [PT.  i.  17 


apart,  gravity  being  partly  overcome  by  the  force  of  the  elec- 
tric repulsion.  A  couple  of  narrow  strips  of  the  thinnest 
tissue  paper,  hung  upon  a  support,  will  behave  similarly  when 
electrified.  But  better  results  are  obtained  with  two  strips 
of  gold-leaf,  which,  being  excessively  thin,  is  much  lighter 
than  the  thinnest  paper.  Aluminium  leaf  is  even  better. 
The  Gold-Leaf  Electroscope  is  conveniently  made  by  sus- 
pending the  two  leaves  within  a  wide-mouthed  glass  jar, 


FIG.  12.  —  Gold-Leaf  Electroscope. 

which  serves  both  to  protect  them  from  draughts  of  air  and 
to  support  them  from  contact  with  the  ground.  The  mouth 
of  the  jar  should  be  closed  by  a  plug  of  paraffin  wax,  through 
which  is  pushed  a  bit  of  varnished  glass  tube.  Through  this 
passes  a  stiff  brass  wire,  the  lower  end  of  which  is  bent  at  a 
right  angle  to  receive  the  two  strips  of  gold-leaf,  while  the 
upper  supports  a  flat  plate  of  metal,  or  may  be  furnished  with 
a  brass  knob.  When  kept  dry  and  free  from  dust  this  instru- 
ment will  indicate  excessively  small  quantities  of  electrifica- 
tion. A  rubbed  glass  rod,  even  while  two  or  three  feet  away, 
will  cause  the  leaves  to  repel  one  another.  The  chips  pro- 


CH.  i.  17]  GOLD-LEAF   ELECTROSCOPE  17 

duced  by  sharpening  a  pencil,  falling  on  the  electroscope  top, 
are  found  to  be  electrified.  If  the  knob  be  brushed  with  a 
small  camers-hair  brush,  even  this  slight  friction  produces 
a  perceptible  effect.  With  this  instrument  all  kinds  of  fric- 
tion can  be  shown  to  produce  electrification.  Let  a  person, 
standing  upon  an  insulating  support  —  such  as  a  stool  with 
glass  legs,  or  a  board  supported  on  four  glass  tumblers  —  be 
briskly  struck  with  a  silk  handkerchief,  or  with  a  fox's  tail, 
or  even  brushed  with  a  clothes  brush,  he  will  be  electrified, 
as  will  be  indicated  by  the  electroscope  if  he  place  one  hand 
on  the  knob  at  the  top  of  it.  The  Gold-Leaf  Electroscope 
can  further  be  used  to  indicate  the  kind  of  electrification  on  an 
excited  body.  Thus,  suppose  we  rubbed  a  piece  of  brown 
paper  with  a  piece  of  indiarubber  and  desired  to  find  out 
whether  the  electrification  excited  on  the  paper  was  +  or  — , 
we  should  proceed  as  follows  :  —  First  charge  the  gold  leaves 
of  the  electroscope  by  touching  the  knob  with  a  glass  rod 
rubbed  on  silk.  The  leaves  diverge,  being  charged  with  + 
electrification.  When  they  are  thus  charged  the  approach 
of  a  body  which  is  positively  electrified  will  cause  them  to 
diverge  still  more  widely ;  while,  on  the  approach  of  one 
negatively  electrified,  they  will  tend  to  close  together.  If 
now  the  brown  paper  be  brought  near  the  electroscope,  the 
leaves  will  be  seen  to  diverge  more,  proving  the  electrification 
of  the  paper  to  be  of  the  same  kind  as  that  with  which  the 
electroscope  is  charged,  or  positive.  Sometimes  the  outer 
surface  of  the  glass  jar  containing  the  gold  leaves  is  covered 
with  wire  gauze  or  strips  of  foil  to  shield  the  leaves  from  the 
influence  of  external  bodies.  A  preferable  way  is  to  use 
glass  of  a  kind  that  conducts. 

The  part  played  by  the  surrounding  medium  in  the  opera- 
tion of  the  electroscope  is  illustrated  by  Fig.  13.  Of  the  elec- 
tric lines  in  the  field  surrounding  the  rubbed  rod  a  number 
will  pass  into  the  metal  cap  of  the  electroscope  and  emerge 
below,  through  the  leaves.  The  nearer  the  rod  is  brought,  the 
greater  will  be  the  number  of  electric  lines  thus  affecting  the 


18 


ELECTRICITY  AND   MAGNETISM        [PT.  i.  18 


FIG.  13.  —  Action  of  Electro- 
scope. 


instrument.  There  being  a  tension  along  the  lines  and  a  pres- 
sure across  them,  the  effect  is  to  draw  the  gold  leaves  apart 
as  though  they  repelled  each  other. 

The  Gold-Leaf  Electroscope  will  also  indicate  roughly 
the  amount  of  electrification  on  a 
body  placed  in  contact  with  it, 
for  the  gold  leaves  open  out  more 
widely  when  the  charge  thus  im- 
parted to  them  is  greater.  For  ex- 
act measurement,  however,  of  the 
amount  of  charge  recourse  must  be 
had  to  the  instruments  known  as 
Electrometers,  described  in  Art.  304, 
pp.  263-269. 

In  another  form  of  electroscope 
(Bohnenberger's)  a  single  gold  leaf 
is  used,  and  is  suspended  between  two  metallic  plates, 
one  of  which  can  be  positively,  the  other  negatively  electri- 
fied, by  placing  them  in  communication  with  the  poles  of  a 
"dry  pile"  (Art.  203).  If  the 
gold  leaf  be  charged  positively 
or  negatively  it  will  be  attracted 
to  one  side  or  the  other,  accord- 
ing to  the  law  of  attraction  and 
repulsion  mentioned  in  Art.  5. 

18.  The  Torsion  Balance.  — 
Although  more  properly  an 
Electrometer  than  a  mere  Elec- 
troscope, it  will  be  most  con- 
venient to  describe  here  the  in- 
strument known  as  the  Torsion 
Balance  (Fig.  14).  This  instru- 
ment, once  famous,  but  now  quite 

obsolete,  serves  to  measure  the  force  of  the  repulsion  be- 
tween two  similarly  electrified  bodies,  by  balancing  the 
repelling  force  against  the  force  exerted  by  a  fine  wire  in 


FIG.  14.  —  Torsion  Balance. 


CH.  i.  18]  THE   TORSION  BALANCE  19 

untwisting  itself  after  it  has  been  twisted.  The  torsion  bal- 
ance consists  of  a  light  arm  or  lever  of  shellac  suspended 
within  a  cylindrical  glass  case  by  means  of  a  fine  silver  wire. 
At  one  end  this  lever  is  furnished  with  a  gilt  pith-ball  n. 
The  upper  end  of  the  silver  wire  is  fastened  to  a  brass  top, 
upon  which  a  circle,  divided  into  degrees,  is  cut.  This  top 
can  be  turned  round  in  the  tube  which  supports  it,  and  is 
called  the  torsion-head.  Through  an  aperture  in  the  cover 
there  can  be  introduced  a  second  gilt  pith-ball  m,  fixed  to 
the  end  of  a  vertical  glass  rod  a.  Round  the  glass  case,  at 
the  level  of  the  pith-balls,  a  circle  is  drawn,  and  divided  also 
into  degrees. 

In  using  the  torsion  balance  to  measure  the  amount  of  a 
charge  of  electricity,  the  following  method  is  adopted :  — 
First,  the  torsion-head  is  turned  round  until  the  two  pith- 
balls  m  and  n  just  touch  one -another.  Then  the  glass  rod 
a  is  taken  out,  and  the  charge  of  electricity  to  be  measured  is 
imparted  to  the  ball  m,  which  is  then  replaced  in  the  balance. 
As  soon  as  m  and  n  touch  one  another,  part  of  the  charge 
passes  from  m  to  n,  and  they  repel  one  another  because  they 
are  then  similarly  electrified.  The  ball  n,  therefore,  is  driven 
round  and  twists  the  wire  up  to  a  certain  extent.  The  force 
of  repulsion  becomes  less  and  less  as  n  gets  farther  and  far- 
ther from  m ;  but  the  force  of  the  twist  gets  greater  and 
greater  the  more  the  wire  is  twisted.  Hence  these  two 
forces  will  balance  one  another  when  the  balls  are  separated 
by  a  certain  distance,  and  it  is  clear  that  a  large  charge  of 
electricity  will  repel  the  ball  n  with  a  greater  force  than  a 
lesser  charge  would.  The  distance  through  which  the  ball  is 
repelled  is  read  off  in  angular  degrees  of  the  scale.  When  a 
wire  is  twisted,  the  force  with  which  it  tends  to  untwist  is 
precisely  proportional  to  the  amount  of  the  twist.  The  force 
required  to  twist  the  wire  ten  degrees  is  just  ten  times  as  great 
as  the  force  required  to  twist  it  one  degree.  In  other  words, 
the  force  of  torsion  is  proportional  to  the  angle  of  torsion.  The 
angular  distance  between  the  two  balls  is,  when  they  are  not 


20  ELECTRICITY   AND   MAGNETISM        [FT.  i.  19 

very  widely  separated,  very  nearly  proportional  to  the  actual 
straight  distance  between  them,  and  represents  the  force 
exerted  between  electrified  balls  at  that  distance  apart.  The 
student  must,  however,  carefully  distinguish  between  the 
measurement  of  the  force  and  the  measurement  of  the  actual 
quantity  of  electricity  with  which  the  instrument  is  charged. 
For  the  force  exerted  between  the  electrified  balls  will  vary 
at  different  distances  according  to  a  particular  law  known  as 
the  "  law  of  inverse  squares,"  which  requires  to  be  carefully 
explained. 

19.  The  Law  of  Inverse  Squares.  —  Coulomb  found,  by 
means  of  the  Torsion  Balance,  that  the  force  exerted  between 
two  small  electrified  bodies  varies  inversely  as  the  square  of 
the  distance  between  them  when  the  distance  is  varied .  Thus, 
suppose  two  small  electrified  bodies  1  inch  apart  repel  one 
another  with  a  certain  force,  at  a  distance  of  2  inches  the  force 
will  be  found  to  be  only  one  quarter  as  great  as  the  force  at  1 
inch  ;  and  at  10  inches  it  will  be  only  T^7  part  as  great  as  at 
1  inch.  This  law  is  demonstrated  by  the  following  experi- 
ment with  the  torsion  balance.  The  two  scales  were  adjusted 
to  0°,  and  a  certain  charge  was  then  imparted  to  the  balls. 
The  ball  n  was  repelled  round  to  a  distance  of  36°.  The 
twist  on  the  wire  between  its  upper  and  lower  ends  was  also 
36°,  or  the  force  tending  to  repel  was  thirty-six  times  as 
great  as  the  force  required  to  twist  the  wire  by  1°.  The  tor- 
sion-head was  now  turned  round  so  as  to  twist  the  thread  at 
the  top  and  force  the  ball  n  nearer  to  ra,  and  was  turned 
round  until  the  distance  between  n  and  m  was  halved.  To 
bring  down  this  distance  from  36°  to  18°,  it  was  found  need- 
ful to  twist  the  torsion-head  through  126°.  The  total  twist 
between  the  upper  and  lower  ends  of  the  wire  was  now 
126°+ 18°,  or  144°;  and  the  force  was  144  times  as  great 
as  that  force  which  would  twist  the  wire  1°.  But  144  is  four 
times  as  great  as  36  ;  hence  we  see  that  while  the  distance  had 
been  reduced  to  one  half,  the  force  between  the  balls  had  be- 
come four  times  as  great.  Had  we  reduced  the  distance  to 


CH.  i.20]  FIELD   BETWEEN  TWO  BALLS  21 

one  quarter,  or  9°,  the  total  torsion  would  have  been  found 
to  be  576,°  or  sixteen  times  as  great ;  showing  the  force  to 
vary  inversely  as  the  square  of  the  distance. 

In  practice  it  requires  great  experience  and  skill  to  obtain 
results  as  exact  as  this,  for  there  are  many  sources  of  inaccu- 
racy in  the  instrument.  The  balls  must  be  very  small,  in 
proportion  to  the  distances  between  them.  The  charges 
of  electricity  on  the  balls  are  found,  moreover,  to  become 
gradually  less  and  less,  as  if  the  electricity  leaked  away  into 
the  air.  This  loss  is  less  if  the  apparatus  be  quite  dry.  It  is 
therefore  usual  to  dry  the  interior  by  placing  inside  the  case 
a  cup  containing  either  chloride  of  calcium,  or  pumice  stone 
soaked  with  strong  sulphuric  acid,  to  absorb  the  moisture. 

Before  leaving  the  subject  of  electric  forces,  it  may  be  well 
to  mention  that  the  force  of  attraction  between  two  oppositely 
electrified  bodies  varies  inversely  as  the  square  of  the  distance 
between  them,  provided  they  are  so  small  compared  with  the 
distance  between  them.  And  in  every  case,  whether  of  at- 
traction or  repulsion,  the  force  at  any  given  distance  is  pro- 
portional to  the  product  of  the  two  quantities  of  electricity 
on  the  bodies.  Thus,  if  we  had  separately  given  a  charge  of 
2  to  the  ball  m  and  a  charge  of  3  to  the  ball  n}  the  force  be- 
tween them  will  be  3  X  2  =  6  times  as  great  as  if  each  had 
had  a  charge  of  1  given  to  it.  It  must  be  remembered, 
however,  that  the  law  of  inverse  squares  is  only  true  when 
applied  to  the  case  of  bodies  so  small,  as  compared  with  the 
distance  between  them,  that  they  are  mere  points.  For  flat, 
large,  or  elongated  bodies  the  law  of  inverse  squares  does  not 
hold  good.  The  attraction  between  two  large  flat  disks  op- 
positely electrified  with  given  charges,  and  placed  near  to- 
gether, does  not  vary  with  the  distance. 

20.  Field  between  two  Balls.  —  The  electric  field  (Art.  14) 
between  two  oppositely  electrified  balls  is  found  (Fig.  15) 
to  consist  of  curved  lines.  By  the  principle  laid  down  in 
Art.  14,  there  is  a  tension  along  these  lines  so  that  they  tend 
not  only  to  draw  the  two  balls  together,  but  also  to  draw 


22  ELECTRICITY  AND   MAGNETISM      [PT.  i.  21,  22 

the  electrifications  on  the  surfaces 
of  the  balls  toward  one  another. 
There  is  also  a  lateral  pressure  in 
the  medium  tending  to  keep  the 
electric  lines  apart  from  one  an- 
other. One  result  of  these  actions 

FIG.  15. -Field  between  Balls.         ^  thftt  the   chargeg  are  no  longer 

equally  distributed  over  the  surfaces,  but  are  more  dense 
on  the  parts  that  approach  most  nearly. 

21.  Unit    Quantity    of   Electricity.  —  In    consequence   of 
these  laws  of  attraction  and  repulsion,  it  is  found  most  con- 
venient to  adopt  the  following  definition  for  that  quantity 
of  electricity  which  we  take  for  a  unit  in  terms  of  which 
to  measure  other  quantities  of  electricity.     One  (electrostatic) 
Unit  of  Electricity  is  that  quantity  which,  when  placed  at  a  dis- 
tance of  one  centimetre  in  air  from  a  similar  and  equal  quantity, 
repels  it  with  a  force  of  one  dyne  (see  Art.  277).     If  instead  of 
air  another  medium  occupies  the  space,  the  force  will  be  dif- 
ferent.    For  example,  if  petroleum  is  used  the  force  exerted 
between  given  charges  will  be  about  half  as  great  (see  Art.  57) . 
Further   information  about  the   measurement  of  electrical 
quantities  is  given  in  Arts.  279  and  317. 

LESSON  III.  —  Electrification  by  Influence 

22.  Influence.  —  We    have    learned    how    two    charged 
bodies  may  apparently  attract  or  repel  one  another  by  virtue 
of  the  charges  they  carry,  and  will  now  consider  the  electric 
influence  exerted  by  an  electrified  body  upon  one  that  has 
not  been  electrified. 

Suppose  we  electrify  positively  a  ball  C,  shown  in  Fig.  16, 
and  hold  it  near  to  a  body  that  has  not  been  electrified, 
what  will  occur  ?  We  take  for  this  experiment  the  apparatus 
shown  on  the  right,  consisting  of  a  long  sausage-shaped  piece 
of  metal,  either  hollow  or  solid,  held  upon  a  glass  support. 
This  "  conductor,"  so  called  because  it  is  made  of  metal 


CH.  i.  22]  INFLUENCE  23 

which  permits  electricity  to  pass  freely  through  it  or  over  its 
surface,  is  supported  on  glass  to  prevent  the  escape  of  elec- 
tricity to  the  earth,  glass  being  a  non-conductor.  The  in- 
fluence of  the  positive  charge  of  the  ball  placed  near  this  con- 
ductor is  found  to  induce  electrification  on  the  conductor, 
which,  although  it  has  not  been  rubbed  itself,  will  be  found 
to  behave  at  its  two  ends  as  an  electrified  body.  The  ends 
of  the  conductor  will  attract  little  bits  of  paper ;  and  if  pith- 
balls  be  hung  to  the  ends  they  are  found  to  be  repelled.  It 


FIG.  16.  —  Experiment  on  Electric  Influence. 

will,  however,  be  found  that  the  middle  region  of  the  long- 
shaped  conductor  will  give  no  sign  of  any  electrification. 
Further  examination  will  show  that  the  two  electrifications 
on  the  ends  of  the  conductor  are  of  opposite  kinds,  that 
nearest  the  excited  glass  ball  being  a  negative  charge,  and  that 
at  the  farthest  end  being  an  equal  charge,  but  of  positive 
sign.  It  appears  then  that  a  positive  charge  attracts  negative 
and  repels  positive,  and  that  this  influence  can  be  exerted  at 
a  distance  from  a  body.  If  we  had  begun  with  a  charge  of 
negative  electrification  upon  a  stick  of  sealing-wax,  the  pres- 
ence of  the  negative  charge  near  the  conductor  would  have 
induced  a  positive  charge  on  the  near  end,  and  negative  on 
the  far  end.  This  action,  discovered  in  1753  by  John  Canton, 


24 


ELECTRICITY   AND   MAGNETISM        [PT.  i.  22 


is  spoken  of  as  influence,  or  electrostatic  induction.1  It  will 
take  place  across  a  considerable  distance.  Even  if  a  large 
sheet  of  clean  dry  glass  be  placed  between  the  charged  body 
and  the  conductor,  the  effect  will  be  produced.  When  the 
electrified  body  is  removed  both  the  charges  disappear  from 
the  conductor,  leaving  no  trace  behind,  and  the  glass  ball  is 
found  to  be  just  as  much  electrified  as  before ;  it  has  parted 
with  none  of  its  own  charge.  It  may  be  noted  that,  accord- 
ing to  the  electron  theory  (see  Art.  630),  a  body  charged 
positively  is  regarded  as  having  fewer  free  electrons  than  the 
things  round  it,  while  one  with  a  negative  charge  is  regarded 
as  having  more.  According  to  this  view  it  would  appear 
that  when  a  body  (such  as  the  -f-  electrified  glass  ball)  having 
fewer  electrons  than  things  around  it  is  placed  near  an  insu- 
lated conductor,  the  uniform  distribution  of  electricity  in 
that  conductor  is  disturbed,  the  electrons  flowing  up  to  that 

end  which  is  near  the  -f  body,  a 
greater  number  than  usual  accumu- 
lating at  that  end,  and  fewer  than 
usual  remaining  at  the  other  end. 
This  view  of  things  will  account  for 
the  disappearance  of  all  signs  of 
electrification  when  the  electrified 
body  is  removed,  for  then  the  distri- 
bution of  electrons  in  the  conductor 
recovers  its  uniformity;  and  the 

conductor  being  neither  more  nor  less  electrified  than  all 
the  objects  around  on  the  surface  of  the  earth,  will  show 


.  17.  —  Charging  by  Influence. 


1  The  word  induction  originally  used  was  intended  to  denote  an  action  at 
a  distance,  as  distinguished  from  conduction,  which  implied  the  conveyance 
of  the  action  by  a  material  conductor.  But  there  were  discovered  other  ac- 
tions at  a  distance,  namely,  the  induction  of  currents  by  moving  magnets, 
or  by  other  currents,  and  the  induction  of  magnetism  in  iron  in  the  presence 
of  a  neighbouring  magnet.  As  the  term  induction  has  now  been  officially 
adopted  for  the  induction  of  electromotive-forces,  its  use  in  other  senses  ought 
to  be  dropped.  Hence  the  preference  now  given  to  the  term  influence  for  the 
induction  of  charges  by  charges. 


CH.  i.  23]  EFFECTS    OF    INFLUENCE  25 

neither  positive  nor  negative  charge.  The  action  is  not, 
however,  a  mere  action  at  a  distance ;  it  is  one  in  which 
the  intervening  medium  takes  an  essential  part.  Consider 
(Fig.  17)  what  takes  place  when  an  insulated,  non-electri- 
fied metal  ball  B  is  brought  under  the  influence  of  a 
positively  electrified  body  A.  At  once  some  of  the  electric 
lines  of  the  field  that  surrounds  A  pass  through  B,  entering 
it  at  the  side  nearer  A,  and  leaving  it  at  the  farther 
side.  As  the  ball  B  has  no  charge  of  its  own,  as  many  electric 
lines  will  enter  on  one  side  as  leave  on  the  other ;  or,  in  other 
words,  the  induced  negative  charge  on  one  side  and  the  in- 
duced positive  charge  on  the  other  will  be  exactly  equal  in 
amount.  They  will  not,  however,  be  quite  equally  distrib- 
uted, the  negative  charge  on  the  side  nearer  A  being  more 
concentrated,  and  the  lines  in  the  field  on  that  side  denser. 

23.  Effects  of  Influence.  —  If  the  conductor  be  made 
in  two  parts,  which,  while  under  the  influence  of  the  electrified 
body,  are  separated,  then  on  the  removal  of  the  electrified 
body  the  two  charges  can  no  longer  return  to  neutralize  one 
another,  but  remain  each  on  its  own  portion  of  the  conductor. 

If  the  conductor  be  not  insulated  on  glass  supports,  but 
placed  in  contact  with  the  ground,  that  end  only  which  is 
nearest  the  electrified  body  will  be  found  to  be  electrified. 
The  repelled  charge  is  indeed  repelled  as  far  as  possible  into 
the  walls  of  the  room ;  or,  if  the  experiment  be  performed  in 
the  open  air,  into  the  earth.  One  kind  of  electrification  only 
is  under  these  circumstances  to  be  found,  namely,  the  opposite 
kind  to  that  of  the  excited  body,  whichever  this  may  be.  The 
same  effect  occurs  in  this  case  as  if  an  electrified  body  had  the 
power  of  attracting  up  the  opposite  kind  of  charge  out  of  the 
earth.  This  is  easily  explained  by  the  electron  theory  (see 
Art.  630).  According  as  the  charge  of  the  body  be  -f  or  -, 
the  electrons  in  the  earth  are  attracted  up  into  the  conductor, 
making  it  -,  or  they  are  repelled  into  the  earth  from  the  con- 
ductor, leaving  it  +. 

The  quantity  of  the  two  charges  separated  by  influence 


26  ELECTRICITY  AND   MAGNETISM         [PT.  i.  24 

on  a  conductor  in  the  presence  of  a  charge  of  electricity,  de- 
pends upon  the  amount  of  the  charge,  and  upon  the  distance 
of  the  charged  body  from  the  conductor.  A  highly  electrified 
glass  rod  will  exert  a  greater  influence  than  a  less  highly  elec- 
trified one ;  and  it  produces  a  greater  effect  as  it  is  brought 
nearer  and  nearer.  The  utmost  it  can  do  will  be  to  induce 
on  the  near  end  a  negative  charge  equal  in  amount  to  its  own 
positive  charge,  and  a  similar  amount  of  positive  electrifica- 
tion at  the  far  end ;  but  usually,  before  the  electrified  body 
can  be  brought  so  near  as  to  do  this,  something  else  occurs 
which  entirely  alters  the  condition  of  things.  As  the  elec- 
trified body  is  brought  nearer  and  nearer,  the  charges  of 
opposite  sign  on  the  two  opposed  surfaces  attract  one  another 
more  and  more  strongly  and  accumulate  more  and  more 
densely,  until,  as  the  electrified  body  approaches  very  near, 
a  spark  is  seen  to  dart  across,  the  two  charges  rushing  together 
to  neutralize  one  another,  leaving  the  induced  charge  of  posi- 
tive electricity,  which  was  formerly  repelled  to  the  other  end 
of  the  conductor,  as  a  permanent  charge. 

In  Fig.  18  is  illustrated  the  operation  of  gradually  lower- 
ing down  over  a  table  a  positively  electrified  metal  ball. 
The  nearer  it  approaches  the  table,  the  more  does  the  electric 
field  surrounding  it  concentrate  itself  in  the  gap  between  the 
ball  and  the  table  top;    the  latter  be- 
coming negatively  electrified  by  influ- 
ence.    Where    the    electric    lines    are 
densest  the  tension  in  the  medium  is 
greatest,  until  when  the  ball  is  lowered 
still  further  the  mechanical  resistance  of 
the    air  can  no   longer  withstand   the 
stress ;  it  breaks  down  and  the  layer  of 
FlG-    18OV~  T^if1   BaU  air  is  pierced  by  a  spark.     If  oil  is  used 
as  a  surrounding  medium  instead  of  air, 
it  will  be  found  to  withstand  a  much  greater  stress  without 
being  pierced. 

24.    Attraction  due  to  Influence.  —  We  are  now  able  to 


CH.  i.  25,  26]  THE    ELECTROPHORUS  27 

apply  the  principle  of  influence  to  explain  why  an  electrified 
body  should  attract  things  that  have  not  been  electrified  at 
all.  Fig.  17,  on  p.  24,  may  be  taken  to  represent  a  light 
metal  ball  B  hung  from  a  silk  thread  presented  to  the  end  of 
a  rubbed  glass  rod  A.  The  positive  charge  on  A  produces 
by  influence  a  negative  charge  on  the  nearer  side  of  B  and  an 
equal  positive  charge  on  the  far  side  of  B.  The  nearer 
half  of  the  ball  will  therefore  be  attracted,  and  the  farther 
half  repelled ;  but  the  attraction  will  be  stronger  than  the 
repulsion,  because  the  attracted  charge  is  nearer  than  the 
repelled.  Hence  on  the  whole  the  ball  will  be  attracted.  It 
can  easily  be  observed  that  if  a  ball  of  non-conducting  sub- 
stance, such  as  wax,  be  employed,  it  is  not  attracted  so  much 
as  a  ball  of  conducting  material.  This  in  itself  proves  that 
influence  really  precedes  attraction. 

Another  way  of  stating  the  facts  is  as  follows :  —  The 
tension  along  the  electric  field  on  the  right  of  B  will  be 
greater  than  that  on  the  left,  because  of  the  greater  concen- 
tration of  the  electric  lines  on  the  right. 

25.  Dielectric    Action.  —  We   have    pointed    out   several 
times  what  part  the  intervening  medium  plays  in  these  ac- 
tions at  a  distance.     The  air,  oil,  glass,  or  other  material 
between  does  not  act  simply  as  a  non-conductor;    it  takes 
part  in  the  propagation  of  the  electric  forces.     Hence  Fara- 
day, who  discovered  this  fact,  termed  such  materials  dielec- 
trics.    Had  oil,  or  solid  sulphur,  or  glass,  been  used  instead 
of  air,  the  influence  exerted  by  the  presence  of  the  electrified 
body  at  the  same  distance  would  have  been  greater.     The 
ability  of  a  non-conducting  substance  to  transmit  the  influence 
of  an  electrified  body  across  it  is  called  its  inductivity  (or  was 
formerly  called  its  specific  inductive  capacity,  see  Art.  57  and  ' 
Lesson  XXIII.). 

26.  The  Electrophorus.  —  We  are  now  prepared  to  ex- 
plain the  operation  of  a  simple  and  ingenious  instrument, 
devised  by  Volta  in  1775,  for  the  purpose  of  procuring,  by 
the  principle  of  influence,  an  unlimited  number  of  charges 


28 


ELECTRITICY   AND   MAGNETISM 


[PT.  i.  26 


of  electricity  from  one  single  charge.  This  instrument x 
is  the  Electrophorus  (Fig.  19).  It  consists  of  two  parts,  a 
round  cake  of  resinous  material  cast  in  a  metal  dish  or  "  sole," 
about  12  inches  in  diameter,  and  a  round  disk  of  slightly 
smaller  diameter  made  of  metal,  or  of  wood  covered  with  tin- 
foil, and  provided  with  a  glass  handle.  Shellac,  or  sealing- 
wax,  or  a  mixture  of  resin,  shellac,  and  Venice  turpentine, 

may  be  used  to  make 
the  cake.  A  slab  of 
sulphur  will  also  an- 
swer, but  it  is  liable 
to  crack.  Sheets  of 
hard  ebonized  in- 
diarubber  are  ex- 
cellent; but  the 
surface  of  this  sub- 
stance requires  oc- 
casional washing 
with  ammonia  and 
rubbing  with  par- 
affin oil,  as  the  sul- 
phur contained  in  it 
is  liable  to  oxidize 
and  to  absorb  mois- 
ture. To  use  the 
electrophorus  the 
resinous  cake  must 
be  beaten  or  rubbed  with  a  warm  piece  of  woollen  cloth, 
or,  better  still,  with  a  cat's  skin.  The  disk  or  "  cover  " 
is  then  placed  upon  the  cake  touched  momentarily  with  the 
ringer,  then  removed  by  taking  it  up  by  the  glass  handle, 
when  it  is  found  to  be  powerfully  electrified  with  a  positive 
charge,  so  much  so  indeed  as  to  yield  a  spark  when  the 

1  Volta's  electrophorus  was  announced  in  1775.  Its  principle  had  already 
been  anticipated  by  Wilcke,  who  in  1762  described  to  the  Swedish  Academy 
of  Sciences  two  "  charging-machines  "  working  by  influence. 


FIG.  19.  —  Volta's  Electrophorus. 


CH.  i.  26]  THE   ELECTROPHORUS  29 

knuckle  is  presented  to  it.  The  "  cover "  may  be  re- 
placed, touched,  and  once  more  removed,  and  will  thus 
yield  any  number  of  sparks,  the  original  charge  on  the 
resinous  plate  meanwhile  remaining  practically  as  strong  as 
before. 

The  theory  of  the  electrophorus  is  very  simple,  provided 
the  student  has  clearly  grasped  the  principle  of  influence 
explained  above.  When  the  resinous  cake  is  first  beaten 
with  the  cat's  skin  its  surface  is  negatively  electrified,  as  in- 
dicated in  Fig.  20.  When  the  metal  disk  is  placed  down  upon 
it,  it  rests  really  only  on  three  or  four  points  of  the  surface, 
and  may  be  regarded  as  an  insulated  conductor  in  the  pres- 
ence of  an  electrified  body.  The  negative  electrification  of 
the  cake  therefore  acts  by  influence  on  the  metallic  disk  or 
"  cover/'  the  electrons  in  it  being  displaced  upwards,  causing 


FIG.  20.  FIG.  21. 

Action  of  Electrophorus. 


the  upper  side  to  become  negatively  electrified,  and  leaving 
a  positive  charge  on  the  under  side.  This  state  of  things 
is  shown  in  Fig.  21.  If  now  the  cover  be  touched  for  an  in- 
stant with  the  finger,  the  negative  charge  of  the  upper  surface 
will  flow  away  to  the  earth  through  the  hand  and  body  of  the 
experimenter.  The  attracted  positive  charge  will,  however, 
remain,  being  bound  as  it  were  by  its  attraction  towards  the 
negative  charge  on  the  cake.  Fig.  22  shows  the  condition  of 
things  after  the  cover  has  been  touched.  If,  finally,  the  cover 
be  lifted  by  its  handle,  the  remaining  positive  charge  will  be 
no  longer  "  bound  "  on  the  lower  surface  by  attraction,  but 
will  distribute  itself  on  both  sides  of  the  cover  (Fig.  23), 
and  may  be  used  to  give  a  spark,  as  already  said.  It  is  clear 


30  ELECTRICITY  AND   MAGNETISM        [PT.  i.  26 

that  no  part  of  the  original  charge  has  been  consumed  in  the 
process,  which  may  be  repeated  as  often  as  desired.  As  a 
matter  of  fact,  the  charge  on  the  cake  slowly  dissipates  — 
especially  if  the  air  be  damp.  Hence  it 'is  needful  sometimes 
to  renew  the  original  charge  by  afresh  beating  the  cake  with 
the  cat's  skin.  The  labour  of  touching  the  cover  with  the 
finger  at  each  operation  may  be  saved  by  having  a  pin  of  brass 
or  a  strip  of  tinfoil  projecting  from  the  metallic  "  sole  "  to  the 
top  surface  of  the  cake,  so  that  it  touches  the  plate  each  time, 


r  f  T  T  r 


FIG.  22.  FIG.  23. 

Action  of  Electrophorus. 

and  thus  neutralizes  the  negative  charge  by  allowing  electrons 
to  flow  away  to  the  earth. 

The  principle  of  the  electrophorus  may  then  be  summed 
up  in  the  following  sentence.  A  conductor  if  touched  while 
under  the  influence  of  a  charged  body  acquires  thereby  a  charge 
of  opposite  sign.1 

Since  the  electricity  thus  yielded  by  the  electrophorus 
is  not  obtained  at  the  expense  of  any  part  of  the  original 
charge,  it  is  a  matter  of  some  interest  to  inquire  what  the 
source  is  from  which  the  energy  of  this  apparently  unlimited 

1  Priestley,  in  1767,  stated  this  principle  in  the  following  language:  — 
"The  electric  fluid,  when  there  is  a  redundancy  of  it  in  any  body,  repels 
the  electric  fluid  in  any  other  body,  when  they  are  brought  within  the 
sphere  of  each  other's  influence,  and  drives  it  into  the  remote  parts  of  the 
body;  or  quite  out  of  the  body,  if  there  be  any  outlet  for  that  purpose. 
In  other  words,  bodies  immerged  in  electric  atmospheres  always  become 
possessed  of  the  electricity,  contrary  to  that  of  the  body  in  whose  atmos- 
phere they  are  immerged." 


CH.  i.  27]  FREE   AND   BOUND    CHARGES  31 

supply  is  drawn  ;  for  it  cannot  be  called  into  existence  without 
the  expenditure  of  some  other  form  of  energy,  any  more  than 
a  steam-engine  can  work  without  fuel.  As  a  matter  of  fact 
it  is  found  that  a  little  more  work  is  required  to  lift  up  the 
cover  when  it  is  charged  than  if  it  were  not  charged;  for, 
when  charged,  there  is  the  tension  of  the  electric  field  to  be 
overcome  as  well  as  the  force  of  gravity.  Slightly  harder 
work  is  done  at  the  expense  of  the  muscular  energies  of  the 
operator ;  and  this  is  the  real  origin  of  the  energy  stored  up 
in  the  separated  charges.  The  purely  mechanical  actions  of 
putting  down  the  disk  on  the  cake,  touching  it,  and  lifting  it 
up,  can  be  performed  automatically  by  suitable  mechanical 
arrangements,  which  render  the  production  of  these  inductive 
charges  practically  continuous.  Of  such  continuous  elec- 
trophori,  the  latest  is  Wimshurst's  machine,  described  in 
Lesson  V. 

27.  "  Free  "  and  "  Bound  "  Electrification.  —  We  have 
spoken  of  a  charge  of  electricity  on  the  surface  of  a  conductor, 
as  being  "  bound  "  when  it  is  attracted  by  the  presence  of  a 
neighbouring  charge  of  the  opposite  kind.  The  converse 
term  "  free  "  is  sometimes  applied  to  the  ordinary  state  of 
electricity  upon  a  charged  conductor,  not  in  the  presence  of  a 
charge  of  an  opposite  kind.  A  "  free  "  charge  upon  an  insu- 
lated conductor  disappears  instantaneously  if  a  conducting 
channel  to  the  earth  be  provided.  It  is  immaterial  what 
point  of  the  conductor  be  touched.  In  the  case  represented 
in  Fig.  17,  lines  of  force  run  out  in  all  directions  from  the  + 
electrified  body  to  the  surrounding  objects.  Some  lines 
encounter  the  metal  ball,  inducing  a  —  charge  where  they 
enter,  and  a  +  charge  on  the  other  side  where  they  pass 
out.  If  the  metal  ball  be  touched  with  the  hand  and  thus 
put  in  connection  with  the  surroundings,  these  latter  lines 
vanish,  and  with  them  the  +  charge  on  the  ball ;  but  the  - 
charge  remains  as  if  it  were  "  bound."  The  4-  charge  is 
"  free  "  to  be  removed,  no  matter  what  part  of  the  metal  ball 
is  touched. 


32  ELECTRITICY  AND   MAGNETISM        [PT.  i.  28 

28.  Method  of  charging  the  Gold-Leaf  Electroscope  by 
Influence.  —  The  student  will  now  be  prepared  to  under- 
stand the  method  by  which  a  Gold-Leaf  Electroscope 
can  be  charged  with  the  opposite  kind  of  charge  to  that 
of  the  electrified  body  used  to  charge  it.  In  Lesson  II. 
it  was  assumed  that  the  way  to  charge  an  electroscope 
was  to  place  the  excited  body  in  contact  with  the  knob, 
and  thus  permit,  as  it  were,  a  small  portion  of  the  charge 
to  flow  into  the  gold  leaves.  A  rod  of  glass  rubbed  on  silk 
being  +  would  thus  obviously  impart  +  electrification  to 
the  gold  leaves. 

Suppose,  however,  the  rubbed  glass  rod  to  be  held  a  few 
inches  above  the  knob  of  the  electroscope,  as  is  indeed  shown 
in  Fig.  13.  Even  at  this  distance  the  gold  leaves  diverge, 
and  the  effect  is  due  to  influence.  The  gold  leaves,  and  the 
brass  wire  and  knob,  form  one  continuous  conductor,  insu- 
lated from  the  ground  by  the  glass  jar.  The  presence  of  the 
-h  charge  of  the  glass  acts  inductively  on  this  "  insulated 
conductor,"  inducing  —  electrification  on  the  near  end  or 
knob,  and  inducing  +  at  the  far  end,  i.e.  on  the  gold  leaves, 
which  diverge.  As  is  shown  in  Fig.  13,  p.  18,  lines  of  force 
pass  from  the  glass  rod  to  the  knob,  and  continue  from  the 
gold  leaves  to  the  floor  and  walls  of  the  case,  and  through 
them  to  the  earth.  If  now,  while  the  excited  rod  is  still  held 
in  position,  the  knob  be  momentarily  touched  with  the  finger, 
and  thereby  put  in  electrical  connection  with  the  earth,  the 
lines  of  force  between  the  earth  and  the  gold  leaves  disap- 
pear, and  the  leaves  collapse  together.  After  removing  the 
finger,  let  the  glass  rod  be  taken  right  away ;  the  lines  of  force 
will  be  dragged  after  it,  and  as  they  increase  in  length  they 
repel  one  another  more  strongly,  until,  when  the  rod  is  so  far 
away  that  it  becomes  part  of  the  surroundings,  lines  of  force 
run  in  from  all  sides  to  the  electroscope,  some  entering  the 
gold  leaves,  which  again  diverge.  And  now  the  charge  upon 
them  is  of  the  same  sign  as  the  charge  upon  the  knob,  namely 
negative. 


CH.  i.  29,  30] 


CONDUCTION 


33 


29.  The  "  Return-Shock."  -  It  is  sometimes  noticed 
that,  when  a  charged  conductor  is  suddenly  discharged,  a 
discharge  is  felt  by  persons  standing  near,  or  may  even  affect 
electroscopes,  or  yield  sparks.  This  action,  known  as  the 
"  return-shock,"  is  due  to  influence.  For  in  the  presence  of  a 
charged  conductor  a  charge  of  opposite  sign  will  be  induced 
in  neighbouring  bodies,  and  on  the  discharge  of  the  conductor 
these  neighbouring  bodies  may  also  suddenly  discharge  their 
induced  charge  into  the  earth,  or  into  other  conducting 
bodies.  A  "  return-shock  "  is  sometimes  felt  by  persons 
standing  on  the  ground  at  the  moment  when  a  flash  of  light- 
ning has  struck  an  object  some  distance  away. 


LESSON  IV.  —  Conduction  and  Distribution  of  Electricity 

30.    Conduction.  —  Toward  the  close  of  Lesson  I.  we  ex- 
plained how  certain  bodies,  such  as  the  metals,   conduct 


Conduction  of  Electrification  by  a  Thread. 


electricity,  while  others  are  non-conductors  or  insulators. 
This  discovery  is  due  to  Stephen  Gray ;  who,  in  1729,  found 
that  a  cork,  inserted  into  the  end  of  a  rubbed  glass  tube, 
and  even  a  rod  of  wood  stuck  into  the  cork,  possessed  the 


34  ELECTRICITY  AND   MAGNETISM        [PT.  i.  30 

power  of  attracting  light  bodies.  He  found,  similarly,  that 
metallic  wire  and  moist  pack-thread  conducted  electricity, 
while  silk  did  not. 

We  may  repeat  these  experiments  by  taking  (as  in  Fig. 
24)  a  glass  rod,  fitted  with  a  cork  and  a  piece  of  wood.  If  a 
bullet  or  a  brass  knob  be  hung  to  the  end  of  this  by  a  linen 
thread  or  a  wire,  it  is  found  that  when  the  glass  tube  is  rubbed 
the  bullet  acquires  the  property  of  attracting  light  bodies. 
If  a  dry  silk  thread  is  used,  however,  no  electricity  will  flow 
down  to  the  bullet. 

Gray  even  succeeded  in  transmitting  a  charge  of  electricity 
through  a  hempen  thread  over  700  feet  long,  suspended  on 
silken  loops.  A  little  later  Du  Fay  succeeded  in  sending  elec- 
tricity to  no  less  a  distance  than  1256  feet  through  a  mois- 
tened thread,  thus  proving  the  conducting  power  of  moisture. 
From  that  time  the  classification  of  bodies  into  conductors 
and  insulators  has  been  observed. 

This  distinction  cannot,  however,  be  entirely  maintained, 
as  a  large  class  of  substances  occupy  an  intermediate  place  as 
partial  conductors.  For  example,  dry  wood  is  a  bad  conduc- 
tor and  also  a  bad  insulator ;  it  is  a  good  enoug  hconductor 
to  conduct  away  the  high-potential  electricity  obtained  by 
friction,  but  it  is  a  bad  conductor  for  the  relatively  low- 
potential  electricity  of  small  voltaic  batteries.  Substances 
that  are  very  bad  conductors  are  said  to  offer  a  great  resist- 
ance to  the  flow  of  electricity  through  them.  There  is  indeed 
no  substance  so  good  a  conductor  as  to  be  devoid  of  resist- 
ance. There  is  no  substance  of  so  great  a  resistance  as  not 
to  conduct  a  little.  Even  silver,  which  conducts  best  of 
all  known  substances,  resists  the  flow  of  electricity  to  a  small 
extent ;  and,  on  the  other  hand,  such  a  non-conducting  sub- 
stance as  glass,  though  its  resistance  is  many  million  times 
greater  than  that  of  any  metal,  does  allow  a  very  minute 
quantity  of  electricity  to  pass  through  it.  In  the  following 
list,  the  substances  named  are  placed  in  order,  each  conduct- 
ing better  than  those  lower  down  on  the  list. 


CH.  I.  31] 


CONDUCTORS 


35 


Silver 
Copper 
Aluminium 
Other  metals 
Carbon 
Liquid  acids 
Liquid  alkalis     . 
Salts  in  solution 
Water  (impure) 

Cotton 
Dry  wood 
Marble 
Paper 


3 


Pure  water 

Oils   . 

Porcelain  . 

Wool 

Silk 

Resin 

Indiarubber 

Guttapercha 

Shellac 

Ebonite 

Paraffin  Wax 

Glass 

Quartz  (fused) 

Air  and  gases 


A  simple  way  of  observing  experimentally  whether  a  sub- 
stance is  a  conductor  or  not,  is  to  take  a  charged  gold-leaf 
electroscope,  and,  holding  the  substance  to  be  examined  in 
the  hand,  touch  the  knob  of  the  electroscope  with  it.  If  the 
substance  is  a  conductor  the  electrons  can  flow  away  through 
it  and  through  the  body  to  (or  from)  the  earth,  and  the 
electroscope  will  be  discharged.  Through  good  conductors 
the  rapidity  of  the  flow  is  so  great  that  the  discharge  is  prac- 
tically instantaneous.  Further  information  on  this  question 
is  given  in  Lesson  XXXIII,  p.  400. 

31.  Distribution  of  Charge  on  Bodies.  —  If  electrification 
is  produced  at  one  part  of  a  non-conducting  body,  it  remains 
at  that  point  and  does  not  flow  over  the  surface,  or  at  most 
flow's  over  it  exceedingly  slowly.  Thus  if  a  glass  tube  is 
rubbed  at  one  end,  only  that  one  end  is  electrified.  Hot 
glass  is,  however,  a  conductor.  If  a  warm  cake  of  resin  be 
rubbed  at  one  part  with  a  piece  of  cloth,  only  the  portion 
rubbed  will  attract  light  bodies,  as  may  be  proved  by  dusting 
upon  it  through  a  piece  of  muslin  fine  powders  such  as  red 
lead,  lycopodium,  or  verdigris,  which  adhere  where  the  sur- 
face is  electrified.  The  case  is,  however,  wholly  different 
when  a  charge  of  electricity  is  imparted  to  any  part  of  a 
conducting  body  placed  on  an  insulating  support,  for  the 


36 


ELECTRICITY   AND   MAGNETISM 


[PT.  i.  32 


charge  instantly  distributes  itself  all  over  the  surface,  though 
in  general  not  uniformly  over  all  parts  of  the  surface. 

32.  The  Charge  resides  on  the  Surface.  —  A  charge  of 
electricity  resides  on  the  surface  only  of  conducting  bodies. 
This  is  proved  by  the  fact  that  it  is  found  to  be  immaterial 


FIG.  25.  —  Examining  Charges  by  a  Proof-plane. 

to  the  distribution  what  the  interior  of  a  conductor  is  made  of ; 
it  may  be  solid  metal,  or  hollow,  or  even  consist  of  wood  cov- 
ered with  tinfoil  or  gilt ;  but,  if  the  shape  be  the  same,  the 
charge  will  distribute  itself  precisely  in  the  same  manner  over 
the  surface.  There  are  also  several  ways  of  proving  by  direct 
experiment  this  very  important  fact.  Let  a  hollow  metal 
ball,  having  an  aperture  at  the  top,  be  taken  (as  in  Fig.  25), 
and  set  upon  an  insulating  stem,  and  charged  by  sending 
into  it  a  few  sparks  from  an  electrophorus.  The  absence  of 
any  charge  in  the  interior  may  be  shown  as  follows :  —  In 


CH.  i.  33]  CHARGE    ON    SURFACE  37 

order  to  observe  the  nature  of  the  electrification  of  a  charged 
body,  it  is  convenient  to  have  some  means  of  removing  a 
small  quantity  of  the  charge  as  a  sample  for  examination. 
To  obtain  such  a  sample,  a  little  instrument  known  as  a 
proof-plane  is  employed.  It  consists  of  a  little  disk  of  sheet 
copper  or  of  gilt  paper  fixed  at  the  end  of  a  small  glass  rod. 
If  this  disk  is  laid  on  the  surface  of  an  electrified  body  at  any 
point,  part  of  the  charge  flows  into  it,  and  it  may  be  then 
removed,  and  the  sample  thus  obtained  may  be  examined 
with  a  gold-leaf  electroscope  in  the  ordinary  way.  For  some 
purposes  a  metallic  bead,  fastened  to  the  end  of  a  glass  rod, 
is  more  convenient  than  a  flat  disk.  If  such  a  proof-plane 
be  applied  to  the  outside  of  our  electrified  hollow  ball,  and 
then  touched  on  the  knob  of  an  electroscope,  the  gold  leaves 
will  diverge,  showing  the  presence  of  a  charge.  But  if  the 
proof-plane  be  carefully  inserted  through  the  opening,  and 
touched  against  the  inside  of  the  globe  and  then  withdrawn, 
it  will  be  found  that 
the  inside  is  destitute  / 

of  electrification.  An 
electrified  pewter  mug 
will  show  a  similar  re- 
sult, and  so  will  even 
a  cylinder  of  wire 
gauze. 

33.  Experiment  with 
Hollow    Sphere.  - 
Cavendish   and    Cou- 
lomb proved  the  same 

•   '    ,     .  FIG.  26.  —  Experiment  with  Hollow  Hemispheres. 

tact  in  another  way. 

A  copper  ball  was  electrified  and  insulated.  Two  hollow 
hemispheres  of  copper,  of  a  larger  size,  and  furnished  with 
glass  handles,  were  then  placed  together  outside  it  (Fig.  26). 
So  long  as  they  did  not  come  into  contact  the  charge  re- 
mained on  the  inner  sphere ;  but  if  the  outer  shell  touched 
the  inner  sphere  for  but  an  instant,  the  whole  of  the  charge 


38  ELECTRICITY   AND   MAGNETISM        [PT.  i.  34 

passed  to  the  exterior;  and  when  the  hemispheres  were 
separated  and  removed  the  inner  globe  was  found  to  be  com- 
pletely discharged. 

34.  Further  Explanation.  —  Doubtless  the  explanation  of 
this  behaviour  of  electricity  is  to  be  found  in  the  property 
previously  noticed  as  possessed  by  either  kind  of  electrifica- 
tion, namely,  that  of  repelling  itself ;  hence  it  retreats  as  far 
as  can  be  from  the  centre  and  remains  upon  the  surface.  An 
important  proposition  concerning  the  absence  of  electric  force 
within  a  closed  conductor  is  proved  in  Lesson  XXI ;  mean- 


FIG.  27.  —  Faraday's  Conical  Bag. 

while  it  must  be  noted  that  the  proofs,  so  far,  are  directed 
to  demonstrate  the  absence  of  a  free  charge  of  electricity 
in  the  interior  of  hollow  conductors.  Amongst  other  experi- 
ments, Terquem  showed  that  a  pair  of  gold  leaves  hung 
inside  a  wire  cage  could  not  be  made  to  diverge  when  the 
cage  was  electrified.  Faraday  constructed  a  conical  bag  of 
linen-gauze,  supported  as  in  Fig.  27,  upon  an  insulating  stand, 
and  to  it  silk  strings  were  attached,  by  which  it  could  be 
turned  inside  out.  It  was  charged,  and  the  charge  was 
shown  by  the  proof-plane  and  electroscope  to  be  on  the  out- 
side of  the  bag.  On  turning  it  inside  out  the  electricity  was 
once  more  found  outside.  Faraday's  most  striking  experi- 


CH.  i.  35-37]          ELECTRIFICATION   EXTERNAL  39 

ment  was  made  with  a  hollow  cube,  measuring  12  feet  each 
way,  built  of  wood,  covered  with  tinfoil,  insulated,  and 
charged  by  a  powerful  machine,  so  that  large  sparks  and 
brushes  were  darting  off  from  every  part  of  its  outer  surface. 
Into  this  cube  Faraday  took  his  most  delicate  electroscopes ; 
but  once  within,  he  failed  to  detect  the  least  effect  upon  them. 

35.  Applications.  —  Advantage  is  taken  of  this  in  the  con- 
struction of  delicate  electrometers  and  other  instruments, 
which  can  be  effectually  screened  from  the  influence  of  elec- 
trified bodies  by  enclosing  them  in  a  cover  of  thin  metal, 
closed  all  round,  except  where  apertures  must  be  made  for 
purposes  of  observation.     Metal  gauze  answers  excellently, 
and  is  nearly  transparent.     It  was  proposed   by  the  late 
Professor  Clerk  Maxwell  to  protect  buildings  from  lightning 
by  covering  them  on  the  exterior  with  a  network  of  wires. 

36.  Apparent  Exceptions.  —  There  are  two  apparent  ex- 
ceptions to  the  law  that  electrification  resides  only  on  the 
outside  of  conductors.     (1)  If  there  are  electrified  insulated 
bodies  actually  placed  inside  the  hollow  conductor,  the  pres- 
ence of  these  electrified  bodies  acts  inductively  and  attracts 
the  opposite  kind  of  charge  to  the  inner  side  of  the  hollow 
conductor.     (2)  When  electricity  flows  as  a  current,  it  flows 
through  the  substance  of  the  conductor.     The  law  is  limited 
therefore  to  electricity  at  rest,  —  that  is,  to  statical  charges. 

37.  Faraday's  "  Ice-pail  "  Experiment.  —  One  experiment 
of  Faraday  deserves  notice,  as  showing  the  part  played  by 
influence   in   these   phenomena.     He   gradually   lowered   a 
charged  metallic  ball  into  a  hollow  conductor  connected  by 
a  wire  to  a  gold-leaf  electroscope  (Fig.  28),  and  watched  the 
effect.     A  pewter  ice-pail  being  convenient  for  his  purpose, 
this  experiment  is  continually  referred  to  by  this  name, 
though  any  other  hollow  conductor  —  a  tin  canister  or  a 
silver  mug,  placed  on   a   glass  support  —  would  of  course 
answer  equally  well.     The  following  effects  are  observed  :  — 
Suppose  the  ball  to  have  a  +  charge  :  as  it  is  lowered  into  the 
hollow  conductor  the  gold  leaves  begin  to  diverge,  for  the 


40 


ELECTRICITY   AND   MAGNETISM 


[FT.  i.  38 


presence  of  the  charge  acts  inductively,  and  attracts  a  — 
charge  into  the  interior  and  repels  a  +  charge  to  the  exterior. 
The  gold  leaves  diverge  more  and  more  until  the  ball  is  right 
within  the  hollow  conductor,  after  which  no  greater  diver- 
gence is  obtained.  On  letting  the  ball  touch  the  inside  the 
gold  leaves  still  remain  diverging  as  before,  and  if  now  the 
ball  is  pulled  out  it  is  found  to  have  lost  all  its  electrification. 
The  fact  that  the  gold  leaves  diverge  no  wider  after  the  ball 
touched  than  they  did  just  before,  proves  that  when  the 
charged  ball  is  right  inside  the  hollow  conductor  the  induced 
charges  are  each  of  them  precisely  equal  in  amount  to  its  own 
charge,  and  the  interior  negative  charge  exactly  neutralizes 
the  charge  on  the  ball  at  the  moment  when  they  touch, 
leaving  the  equal  exterior  charge  unchanged.  An  electric 

cage,  such  as  this  ice-pail,  when 
connected  with  an  electroscope 
or  electrometer,  affords  an  ex- 
cellent means  of  examining  the 
charge  on  a  body  small  enough 
to  be  hung  inside  it.  For  with- 
out using  up  any  of  the  charge 
of  the  body  (which  we  are 
obliged  to  do  when  applying 
the  method  of  the  proof -plane) 
we  can  examine  the  induced 
charge  repelled  to  the  outside 
of  the  cage,  which  is  equal  in 
amount  and  of  the  same  sign. 
If  two  equal  charges  of  op- 
posite kinds  are  placed  at  the  same  time  within  the  cage  no 
effects  are  produced  on  the  outside. 

38.  Distribution  of  Charge.  —  A  charge  of  electricity  is 
not  usually  distributed  uniformly  over  the  surfaces  of  bodies. 
Experiment  shows  that  the  charge  is  denser  on  the  edges 
and  corners  of  bodies  than  upon  their  flatter  parts.  This 
distribution  can  be  deduced  from  the  theory  laid  down  in 


FIG.  28.  —  Faraday's  Ice-pail 
Experiment. 


CH.  i.  38]  DISTRIBUTION   OF   CHARGE  41 

Lesson  XXI.,  but  meantime  we  will  give  some  of  the  chief 
cases  as  they  can  be  shown  to  exist.  The  term  Electric 
Density  is  used  to  signify  the  amount  of  electricity  at  any 
point  of  a  surface ;  the  electric  density  at  a  point  is  the  number 
of  units  of  electricity  per  unit  of  area  (i.e.  per  square  inch,  or 
per  square  centimetre),  the  distribution  being  supposed  uni- 
form over  this  small  surface. 

(a)  Sphere.  —  The  distribution  of  a  charge  over  an  insulated 
sphere  of  conducting  material  is  uniform,  provided  the  sphere 
is  also  isolated,  that  is  to  say,  is  remote  from  the  presence  of 
all  other  conductors 
and  all  other  elec- 
trified bodies.     The 
density  is  uniform 
all  over  it.     This  is 
symbolized   by  the 
dotted    line    round 
the  sphere  in  Fig. 
29  a,  which  is  at  an 

FIG.  29.  —  Distribution  of  Charges. 

equal  distance  from 

the  sphere  all  round,  suggesting  an  equal  thickness  of  charge 
at  every  point  of  the  surface.  It  must  be  remembered  that 
the  charge  is  not  really  of  any  perceptible  thickness  at  all ; 
it  resides  on  or  at  the  surface,  but  cannot  be  said  to  form  a 
stratum  upon  it. 

(6)  Cylinder  with  rounded  Ends.  —  Upon  an  elongated 
conductor,  such  as  is  frequently  employed  in  electrical  ap- 
paratus (Fig.  296),  the  density  is  greatest  at  the  ends  where 
the  curvature  of  the  surface  is  the  greatest. 

(c)  Two  Spheres  in  contact.  —  If  two  spheres  in  contact 
with  each  other  are  insulated,  and  charged,  it  is  found  that 
the  density  is  greatest  at  the  parts  farthest  from  the  point 
of  contact,  and  least  in  the  crevice  between  them.  If  the 
spheres  are  of  unequal  sizes  the  density  is  greater  on  the 
smaller  sphere,  which  has  the  surface  more  curved  (Fig.  29 c). 
On  an  egg-shaped  or  pear-shaped  conductor  the  density  is 


42  ELECTRICITY   AND   MAGNETISM         [PT.  i.  39 

greatest  at  the  small  end.  On  a  cone  the  density  is  greatest 
at  the  apex ;  and  if  the  cone  terminate  in  a  sharp  point  the 
density  there  is  very  much  greater  than  at  any  other  point. 
At  a  point,  indeed,  the  density  of  the  collected  electricity 
may  be  so  great  as  to  electrify  the  neighbouring  particles  of 
air,  which  then  are  repelled  (see  Art.  47),  thus  producing  a 
continual  loss  of  charge.  For  this  reason  points  and  sharp 
edges  are  always  avoided  on  electrical  apparatus,  except 
where  it  is  specially  desired  to  set  up  a  discharge. 

(d)  Flat  Disk.  —  The  density  of  a  charge  upon  a  flat  disk 
is  greater,  as  we  should  expect,  at  the  edges  than  on  the  flat 
surfaces ;  but  over  the  flat  faces  away  from  the  edge  the  dis- 
tribution is  fairly  uniform  (Fig.  29 d). 

39.  Experimental  Proofs.  —  These  various  facts  are  as- 
certained by  applying  a  small  proof-plane  successively  at 
various  points  of  the  electrified  bodies  and  examining  by 
means  of  an  electroscope  or  electrometer  the  amount  taken 
up  by  the  proof-plane.  Coulomb,  who  investigated  mathe- 
matically as  well  as  experimentally  many  of  the  important 
cases  of  distribution,  employed  the  torsion  balance  (Art.  18) 
to  verify  his  calculations.  He  investigated  thus  the  case  of 
the  ellipsoid  of  revolution,  and  found  the  densities  of  the 
charges  at  the  extremities  of  the  axes  to  be  proportional 
to  the  lengths  of  those  axes.  He  also  showed  that  the 
density  of  the  charge  at  any  other  point  of  the  surface 
of  the  ellipsoid  was  proportional  to  the  length  of  the  per- 
pendicular drawn  from  the  centre  to  the  tangent  at  that 
point.  Riess  found  the  density  at  the  middle  of  the 
edges  of  a  cube  to  be  nearly  two  and  a  half  times  as 
great  as  the  density  at  the  middle  of  a  face ;  while  the 
density  at  a  corner  of  the  cube  was  more  than  four  times 
as  great. 

If  any  portion  of  the  charge  of  an  insulated  conductor  be 
removed,  the  remainder  of  the  charge  will  immediately  re- 
distribute itself  over  the  surface  in  the  same  manner  as  the 
original  charge,  provided  it  be  also  isolated,  i.e.  that  no  other 


CH.  i.  40,  41]      CAPACITY   OF   CONDUCTORS  43 

conductors  or  charged  bodies  be  near  to  perturb  the  distribu- 
tion by  complicated  effects  of  influence. 

40.  Distribution    of   Charge   between    several  Bodies.  — 
If  a  conductor  be  charged  with  any  quantity  of  electricity, 
and  another  conductor  of  the  same  size  and  shape  (but  un- 
charged) be  brought  into  contact  with  it  for  an  instant  and 
then  separated,  it  will  be  found  that  the  charge  has  divided 
itself  equally  between  them.     In  the  same  way  a  charge  may 
be  divided  equally  into  three  or  more  parts  by  being  dis- 
tributed simultaneously  over  three  or  more  equal  and  similar 
conductors  brought  into  contact  and  symmetrically  placed. 

If  two  equal  metal  balls,  suspended  by  silk  strings,  charged 
with  unequal  quantities  of  electricity,  are  brought  for  an 
instant  into  contact  and  then  separated,  it  will  be  found  that 
the  charge  has  redistributed  itself  fairly,  half  the  sum  of  the 
two  charges  being  now  the  charge  of  each.  This  may  even 
be  extended  to  the  case  of  charges  of  opposite  signs.  Thus, 
suppose  two  similar  conductors  to  te  electrified,  one  with  a 
positive  charge  of  5  units  and  the  other  with  3  units  of  nega- 
tive charge,  when  these  are  made  to  touch  and  separated, 
each  will  have  a  positive  charge 'of  1  unit ;  for  the  algebraic 
sum  of  +  5  and  —  3  is  +  2,  which,  shared  between  the  two 
equal  conductors,  leaves  +  1  for  each. 

41.  Capacity  of  Conductors.  —  If  the  conductors  be  un- 
equal in  size,  or  unlike  in  form,  the  shares  taken  by  each  in 
this  redistribution  will  not  be  equal,  but  will  be  proportional 
to  the  respective  capacities  of  the  conductors.     The  defini- 
tion of  capacity  in  its  relation  to  electric  quantities  is  given 
in  Lesson  XXI.,  Art.  289.     We  may,  however,  make  the 
remark,  that  two  insulated  conductors  of  the  same  form,  but 
of  different  sizes,  differ  in  their  electrical  capacity ;    for  the 
larger  one  must  have  a  larger  amount  of  electricity  imparted 
to  it  in  order  to  electrify  its  surface  to  the  same  degree.     The 
term  potential  is  employed  in  this  connection,  in  the  following 
way :  —  A  given   quantity  of  electricity  will   electrify  an 
isolated  body  up  to  a  certain  "  potential  "  (or  its  ability  to  do 


44  ELECTRICITY   AND   MAGNETISM         [PT.  i.  42 

electric  work)  depending  on  its  capacity.  A  large  quantity 
of  electricity  imparted  to  a  conductor  of  small  capacity  will 
electrify  it  up  to  a  very  high  potential;  just  as  a  large  quan- 
tity of  water  poured  into  a  vessel  of  narrow  capacity  will 
raise  the  surface  of  the  water  to  a  high  level  in  the  vessel. 
The  exact  definition  of  Potential,  in  terms  of  energy  spent 
against  the  electrical  forces,  is  given  in  the  lesson  on  Electro- 
statics (Art.  280,  p.  242). 

It  will  be  found  convenient  to  refer  to  a  positively  elec- 
trified body  as  one  electrified  to  a  positive  or  high  potential; 
while  a  negatively  electrified  body  may  be  looked  upon  as  one 
electrified  to  a  low  or  negative  potential.  And  just  as  we  take 
the  level  of  the  sea  as  a  zero  level,  and  measure  the  heights  of 
mountains  above  it,  and  the  depths  of  mines  below  it,  using 
the  sea  level  as  a  convenient  point  of  reference  for  differences 
of  level,  so  we  take  the  potential  of  the  earth's  surface  (for 
the  surface  of  the  earth  is  always  electrified  to  a  certain  de- 
gree) as  zero  potential,  and  use  it  as  a  convenient  point  of 
reference  from  which  to  measure  differences  of  electric 
potential. 

LESSON  V.  —  Electric  Machines 

42.  Frictional  Machines.  —  For  the  purpose  of  procuring 
larger  charges  of  electricity  than  can  be  obtained  by  the 
rubbing  of  a  rod  of  glass  or  shellac,  electric  machines  have 
been  devised.  Electric  machines  are  of  two  1  kinds  :  (1)  Fric- 
tional Machines,  (2)  Influence  Machines.  All  frictional 
machines  consist  of  two  parts,  one  for  producing,  the  other 
for  collecting,  the  electric  charges.  Experience  has  shown 
that  the  quantities  of  -f-  and  —  electrification  developed  by 
friction  upon  the  two  surfaces  rubbed  against  one  another 
depend  on  the  amount  of  friction,  upon  the  extent  of  the  sur- 
faces rubbed,  and  also  upon  the  nature  of  the  substances  used. 
If  the  two  substances  employed  are  near  together  on  the  list 

1  Machines  for  generating  currents,  known  as  dynamo-electric,  or  magneto- 
electric  machines,  are  not  here  considered.  For  these  see  Art.  507. 


CH.  i.  43]  ELECTRIC   MACHINES  45 

of  electrics  given  in  Art.  7,  the  electrical  effect  of  rubbing 
them  together  will  not  be  so  great  as  if  two  substances  widely 
separated  in  the  series  are  chosen.  To  obtain  the  highest 
effect,  the  most  positive  and  the  most  negative  of  the  sub- 
stances convenient  for  the  construction  of  a  machine  should 
be  taken,  and  the  greatest  available  surface  of  them  should 
be  subjected  to  friction,  the  moving  parts  being  pressed 
against  one  another  with  a  sufficient  pressure. 

The  earliest  form  of  electric  machine  was  devised  by 
Otto  von  Guericke  of  Magdeburg,  and  consisted  of  a  globe 
of  sulphur  fixed  upon  a  spindle,  and  pressed  with  the  dry 
surface  of  the  hands  while  being  made  to  rotate ;  with  this 
he  discovered  the  existence  of  electric  sparks  and  the  repul- 
sion of  similarly  electrified  bodies.  Sir  Isaac  Newton  replaced 
Von  Guericke's  globe  of  sulphur  by  a  globe  of  glass.  A  little 
later  the  form  of  the  machine  was  improved  by  various  Ger- 
man electricians :  Von  Bose  added  a  collector  or  "  prime 
conductor,"  in  the  shape  of  an  iron  tube,  supported  by  a  per- 
son standing  on  cakes  of  resin  to  insulate  him,  or  suspended 
by  silken  strings ;  Winckler  of  Leipzig  substituted  a  leathern 
cushion  for  the  hand  as  a  rubber;  and  Gordon  of  Erfurt 
rendered  the  machine  more  easy  of  construction  by  using 
a  glass  cylinder  instead  of  a  glass  globe.  The  electricity 
was  led  from  the  excited  cylinder  or  globe  to  the  prime 
conductor  by  a  metallic  chain  which  hung  over  against  the 
globe.  A  pointed  collector  was  not  employed  until  after 
Franklin's  famous  researches  on  the  action  of  points.  About 
1760  machines  having  glass  plates  instead  of  cylinders  were 
devised.  All  frictional  machines  are,  however,  now  obsolete, 
having  in  recent  years  been  quite  superseded  by  the  modern 
Influence  Machines. 

43.  The  Cylinder  Frictional  Machine.  —  The  Cylinder 
Frictional  Machine  consists  of  a  glass  cylinder  mounted  on 
a  horizontal  axis  capable  of  being  turned  by  a  handle.  Against 
it  is  pressed  from  behind  a  cushion  of  leather  stuffed  with 
horsehair,  the  surface  of  which  is  covered  with  a  powdered 


46 


ELECTRICITY  AND   MAGNETISM        [PT.  i.  43 


amalgam  of  zinc  or  tin.  A  flap  of  silk  attached  to  the  cushion 
passes  over  the  cylinder,  covering  its  upper  half.  In  front 
of  the  cylinder  stands  the  "  prime  conductor,"  which  is  made 
of  metal,  and  usually  of  the  form  of  an  elongated  cylinder  with 
hemispherical  ends,  mounted  upon  a  glass  stand.  At  the 
end  of  the  prime  conductor  nearest  the  cylinder  is  fixed  a  rod 
bearing  a  row  of  fine  metallic  spikes,  resembling  in  form  a 
rake;  the  other  end  usually  carries  a  rod  terminated  in  a 


FIG.  30.  —  Cylinder  Frictional  Electrical  Machine. 

brass  ball  or  knob.  The  general  aspect  of  the  machine  is 
shown  in  Fig.  30.  When  the  handle  is  turned  the  friction 
between  the  glass  and  the  amalgam-coated  surface  of  the 
rubber  produces  a  copious  electrical  action,  electricity  ap- 
pearing as  a  •+-  charge  on  the  glass,  leaving  the  rubber  with  a 
—  charge.  The  prime  conductor  collects  this  charge  by  the 
following  process  :  The  +  charge  being  carried  round  on  the 
glass  acts  inductively  on  the  long  insulated  conductor,  re- 
pelling a  +  charge  to  the  far  end  ;  leaving  the  nearer  end  —  ly 
charged.  The  effect  of  the  row  of  points  is  to  emit  a  —  ly 
electrified  wind  (see  Art.  47)  towards  the  attracting  +  charge 
upon  the  glass,  which  is  neutralized  thereby ;  the  glass  thus 
arriving  at  the  rubber  in  a  neutral  condition  ready  to  be  again 
excited.  This  action  of  the  points  is  sometimes  described, 
though  less  correctly,  by  saying  that  the  points  collect  the  + 
charge  from  the  glass.  If  it  is  desired  to  collect  also  the  — 


CH.  i.  44]      USE    OF   FRICTIONAL  MACHINES 


47 


charge  of  the  rubber,  the  cushion  must  be  supported  on  an 
insulating  stem  and  provided  at  the  back  with  a  metallic 
knob.  It  is,  however,  more  usual  to  use  only  the  +  charge, 
and  to  connect  the  rubber  by  a  chain  to  "  earth/'  so  allowing 
the  —  charge  to  be  neutralized. 

44.  The  Plate  Frictional  Machine.  —  The  Plate  Machine, 
as  its  name  implies,  is  constructed  with  a  circular  plate  of 
glass  or  of  ebonite,  and  is 
usually  provided  with  two 
pairs  of  rubbers  formed  of 
double  cushions,  pressing  the 
plate  between  them,  placed 
at  its  highest  and  lowest 
point,  and  provided  with  silk 
flaps,  each  extending  over  a 
quadrant  of  the  circle.  The 
prime  conductor  is  either 
double  or  curved  round  to 
meet  the  plate  at  the  two 
ends  of  its  horizontal  di- 
ameter, and  is  furnished  with 
two  sets  of  spikes,  for  the 
same  purpose  as  the  row  of  points  in  the  cylinder  machine. 
A  common  form  of  plate  machine  is  shown  in  Fig.  31.  Its 
advantages  are  that  a  large  glass  plate  is  more  easy  to  con- 
struct than  a  large  glass  cylinder  of  perfect  form,  and  that 
the  length  along  the  surface  of  the  glass  between  the  collect- 
ing row  of  points  and  the  edge  of  the  rubber  cushions  is  greater 
in  the  plate  than  in  the  cylinder  for  the  same  amount  of  sur- 
face exposed  to  friction ;  for,  be  it  remarked,  when  the  two 
charges  thus  separated  have  collected  to  a  certain  extent, 
a  discharge  will  take  place  along  this  surface,  the  length  of 
which  limits  therefore  the  ability  of  the  machine  to  give  a 
long  spark. 

It  is  usual  to  smear  the  surface  of  the  rubber  with  an 
electric  amalgam,  consisting  of  equal  parts  of  tin  and  zinc, 


FIG.  31.  —  Plate  Frictional  Electrical 
Machine. 


48  ELECTRICITY  AND   MAGNETISM     [PT.  i.  45,  46 

mixed  while  molten  with  twice  their  weight  of  mercury. 
Such  amalgams  are  applied  to  the  cushions  with  a  little 
stiff  grease.  They  serve  the  double  purpose  of  conduct- 
ing away  the  negative  charge  separated  upon  the  rubber 
during  the  action  of  the  machine,  and  of  affording  as  a 
rubber  a  substance  which  is  more  powerfully  negative  (see 
list  in  Art.  7)  than  the  leather  or  the  silk  of  the  cushion 
itself. 

45.  Precautions  in  using  Frictional  Machines,  —  Several 
precautions  must  be  observed  in  the  use  of  electrical  machines. 
Damp  and  dust  must  be  scrupulously  avoided.     The  surface 
of  glass  is  hygroscopic ;   hence,  except  in  the  driest  climates, 
it  is  necessary  to  warm  the  glass  surfaces  and  rubbers  to  dis- 
sipate the  film  of  moisture  which  collects.     Glass  stems  for 
insulation  may  be  varnished  with  a  thin  coat  of  shellac  var- 
nish, or  with  paraffin  (solid).     Anhydrous  paraffin  (obtained 
by  dropping  a  lump  of  sodium  into  a  bottle  of  paraffin  oil), 
applied  with  a  bit  of  flannel  to  the  previously  warmed  sur- 
faces, hinders  the  deposit  of  moisture.     A  frictional  machine 
which  has  not  been  used  for  some  months  will  require  fresh 
amalgam  on  its  rubbers.      These  should  be  cleaned  and 
warmed,  a  thin  uniform  layer  of  tallow  is  spread  upon  them, 
and  the  amalgam,  previously  reduced  to  a  fine  powder,  is 
sifted  over  the  surface.     In  spite  of  all  precautions  frictional 
machines  are  uncertain  in  their  behaviour  in  damp  weather. 
This  is  the  main  reason  why  they  have  been  superseded  by 
influence  machines. 

All  points  should  be  avoided  in  apparatus  for  frictional 
electricity  except  where  they  are  expressly  employed,  like 
the  "  collecting  "  spikes  on  the  prime  conductor,  to  let  off  a 
charge  of  electricity.  All  the  rods,  etc.,  in  frictional  appara- 
tus are  therefore  made  with  rounded  knobs. 

46.  Experiments    with    the     Electric     Machine.  —  With 
the  electric  machine  many  pleasing  and  instructive  experi- 
ments are  possible.     The  phenomena  of  attraction  and  re- 
pulsion can  be  shown  upon  a  large  scale.     Fig.  32  represents 


CH.  i.  46]      ELECTRIC    MACHINE    EXPERIMENTS 


49 


FIG.  32.  —  Electrical  Chimes. 


a  device  known  as  the  electric  chimes,1  in  which  two  small 

brass  balls  hung  by  silk  strings  are  set  in  motion  and  strike 

against  the  bells  between  which  they  are  hung.     The  two 

outer  bells  are  hung  by  metallic 

wires  or  chains  to  the  knob  of  the 

machine.     The  third   bell  is  hung 

by  a  silk  thread,  but  communicates 

with  the  ground  by  a  brass  chain. 

The  balls  are  first  attracted  to  the 

electrified  outer  bells,  then  repelled, 

and,  having  discharged  themselves 

against  the  uninsulated  central  bell, 

are  again  attracted,  and  so  vibrate 

to  and  fro. 

By  another  arrangement  small 
figures  or  dolls  cut  out  of  pith  can 
be  made  to  dance  up  and  down  between  a  metal  plate  hung 
horizontally  from  the  knob  of  the  machine,  and  another  flat 
plate  an  inch  or  two  lower  and  communicating  with  "  earth." 

Another  favourite  way  of  exhibiting  electric  repulsion 
is  by  means  of  a  doll  with  long  hair  placed  on  the  machine ; 
the  individual  hairs  stand  on  end  when  the  machine  is 
worked,  being  repelled  from  the  head  and  from  one  another. 
A  paper  tassel  will  behave  similarly  if  hung  to  the  prime  con- 
ductor. The  most  striking  way  of  showing  this  phenomenon 
is  to  place  a  person  upon  a  glass-legged  stool,  making  him 
touch  the  knob  of  the  machine ;  when  the  machine  is  worked, 
his  hair,  if  dry,  will  stand  on  end.  Sparks  will  pass  freely 
between  a  person  thus  electrified  and  one  standing  upon  the 
ground. 

The  sparks  from  the  machine  may  be  made  to  kindle  spirits 
of  wine  or  ether,  placed  in  a  metallic  spoon,  connected  by  a 
wire  with  the  nearest  metallic  conductor  that  runs  into  the 

1  Invented  in  1752  by  Franklin,  for  the  purpose  of  warning  him  of  the 
presence  of  atmospheric  electricity,  drawn  from  the  air  above  his  house  by 
a  pointed  iron  rod. 
E 


50 


ELECTRICITY  AND   MAGNETISM        [PT.  i.  47 


ground.  A  gas  jet  may  be  lit  by  passing  a  spark  to  the  burner 
from  the  finger  of  the  person  standing  electrified,  as  just  de- 
scribed, upon  an  insulating  stool. 

47.    Effect  of  Points ;  Electric  Wind.  —  The  effect  of  points 
in  discharging  electricity  from  the  surface  of  a  conductor  may 


FIG.  33.  —  Wind  produced  by  Discharge  at  a  Point. 

be  readily  proved  by  numerous  experiments.  If  the  machine 
be  in  good  working  order,  and  capable  of  giving,  say,  sparks 
4  inches  long  when  the  knuckle  is  presented  to  the  knob,  it 
will  be  found  that,  on  fastening  a 
fine-pointed  needle  to  the  conductor, 
it  discharges  the  electricity  so  effec- 
tually at  its  point  that  only  the 
shortest  sparks  can  be  drawn  at  the 
knob,  while  a  fine  jet  or  brush  of  pale 
blue  light  will  appear  at  the  point. 
If  a  lighted  taper  be  held  in  front  of 
the  point,  the  flame  will  be  visibly 
blown  aside  (Fig.  33)  by  the  streams 
of  electrified  air  repelled  from  the 
point.  These  air-currents  can  be  felt 
with  the  hand.  They  are  due  to  a 
mutual  repulsion  between  the  electrified  air  particles  near  the 
point  and  the  electricity  collected  on  the  point  itself.  That 


FIG.  34.  —  Hamilton's  Mill. 


CH.  i.  48,  49]  INFLUENCE    MACHINES  51 

this  mutual  reaction  exists  is  proved  by  the  electric  fly  or 
electric  reaction-mill  of  Hamilton  (Fig.  34),  which  consists 
of  a  light  cross  of  brass  or  straw,  suspended  on  a  pivot,  and 
having  the  pointed  ends  bent  round  at  right  angles.  When 
placed  on  the  prime  conductor  of  the  machine,  or  joined  to 
it  by  a  chain,  the  force  of  repulsion  between  the  charge  on 
the  points  and  that  on  the  air  immediately  in  front  of  them 
drives  the  mill  round  in  the  direction  opposite  to  that  in 
which  the  points  are  bent.  It  will  even  rotate  if  immersed 
in  turpentine  or  petroleum.  If  the  points  of  the  fly  are 
covered  with  small  round  lumps  of  wax  it  will  not  rotate,  as 
the  presence  of  the  wax  prevents  the  formation  of  any  wind 
or  stream  of  electrified  particles. 

The  electric  wind  from  a  point  will  produce  a  charge  upon 
the  surface  of  any  insulating  body,  such  as  a  plate  of  ebonite 
or  glass,  held  a  few  inches  away.  The  charge  may  be  exam- 
ined by  dusting  red  lead  or  lycopodium  powder  upon  the 
surface.  If  a  slip  of  glass  or  mica  be  interposed  between 
the  point  and  the  surface  against  which  the  wind  is  directed, 
an  electric  shadow  will  be  formed  on  the  surface  at  the  part 
so  screened. 

48.  Armstrong's   Hydro-Electrical   Machine.  —  The  fric- 
tion of  a  jet  of  steam  issuing  from  a  boiler,  through  a  wooden 
nozzle,  generates  electricity.     In  reality  it  is  the  particles  of 
condensed  water  in  the  jet  which  are  directly  concerned. 
Lord  Armstrong,  who  investigated  this  source  of  electricity, 
constructed   a  powerful   apparatus,   known  as  the  hydro- 
electrical  machine,  capable  of  producing  extraordinary  dis- 
charges, yielding  sparks  5  or  6  feet  long.     The  collector  con- 
sisted of  a  row  of  spikes,  placed  in  the  path  of  the  steam  jets 
issuing  from  wooden  nozzles.     It  was  supported,  together 
with  a  brass  ball  which  served  as  prime  conductor,  upon  a 
glass  pillar. 

49.  Influence  Machines.  —  The  second  class  of  electrical 
machines  comprises  those  that  depend  upon  the  principle  of 
influence.     They  also  have  been  termed  convection-induction 


52  ELECTRICITY   AND   MAGNETISM        [PT.  i.  4ft 

machines,  because  they  depend  upon  the  employment  of  a 
minute  initial  charge  which,  acting  by  influence,  induces 
other  charges,  which  are  then  conveyed  by  the  moving  parts  of 
the  machine  to  some  other  part,  where  they  can  be  used  either 
to  increase  the  initial  charge  or  to  furnish  a  supply  of  elec- 
trification to  a  suitable  collector.  Of  such  instruments  the 
oldest  is  the  Electrophorus,  explained  fully  in  Lesson  III. 
Bennet,  Nicholson,  Erasmus  Darwin,  and  others  devised 
pieces  of  apparatus  for  accomplishing  by  mechanism  that 
which  the  electrophorus  accomplishes  by  hand.  Nicholson's 
revolving  doubler,  invented  in  1788,  consists  of  a  revolving 
apparatus,  in  which  an  insulated  carrier  can  be  brought 
into  the  presence  of  an  electrified  body,  there  touched  for 
an  instant  while  under  influence,  then  carried  forward  with 
its  acquired  charge  towards  another  body,  to  which  it  im- 
parts its  charge,  and  which  in  turn  acts  inductively  on  it, 
giving  it  an  opposite  charge,  which  it  can  convey  to  the  first 
body,  thus  increasing  its  initial  charge  at  every  rotation. 

In  the  modern  influence  machines  two  principles  are  em- 
bodied :  (1)  the  principle  of  influence,  namely,  that  a  con- 
ductor touched  while  under  influence  acquires  a  charge  of  the 
opposite  kind ;  (2)  the  principle  of  reciprocal  accumulation. 
This  principle  must  be  carefully  noted.  Let  there  be  two 
insulated  conductors  A  and  B  electrified  ever  so  little,  one 
positively,  the  other  negatively.  Let  a  third  insulated  con- 
ductor C,  which  will  be  called  a  carrier,  be  arranged  to  move 
so  that  it  first  approaches  A  and  then  B,  and  so.  forth.  If 
touched  while  under  the  influence  of  the  small  positive  charge 
on  A  it  will  acquire  a  small  negative  charge ;  suppose  that  it 
then  moves  on  and  gives  this  negative  charge  to  B.  Then 
let  it  be  touched  while  under  the  influence  of  B,  so  acquiring 
a  small  positive  charge.  When  it  returns  towards  A  let  it 
give  up  this  positive  charge  to  A,  thereby  increasing  its  posi- 
tive charge.  Then  A  will  act  more  powerfully,  and  on  re- 
peating the  former  operations  both  B  and  A  will  become 
more  highly  charged.  Each  accumulates  the  charges  de- 


CH.  i.  50] 


INFLUENCE   MACHINES 


53 


rived  by  influence  from  the  other.  This  is  the  fundamental 
action  of  the  machines  in  question.  The  modern  influence 
machines  date  from  1860,  when  C.  F.  Varley  produced  a 
form  with  six  carriers  mounted  on  a  rotating  disk  of  glass. 
This  was  followed  in  1865  by  the  machine  of  Holtz  and  that 
of  Toepler,  and  in  1867  by  those  of  Lord  Kelvin  (the  "  re- 
plenisher  "  and  the  "  mouse-mill  ").  The  influence  machine 

in  widest  use  is  that 
of  Wimshurst. 

50.  Typical  Con- 
struction. —  Before 
describing  some  spe- 
cal  forms  we  will 
deal  with  a  general- 
ized type  of  machine 
having  two  fixed 
field-plates  A  and 
B,  which  are  to  be- 
come respectively 
+  and  — ,  and  a  set 
of  carriers,  attached 
to  a  rotating  disk 
or  armature.  Fig.  35  gives  in  a  diagrammatic  way  a  view  of 
the  essential  parts.  For  convenience  of  drawing  it  is  shown 
as  if  the  metal  field-plates  A  and  B  were  affixed  to  the  outside 
of  an  outer  stationary  cylinder  of  glass,  the  six  carriers  p, 
q,  r,  s,  t,  and  u  being  attached  to  the  inside  of  an  inner  rotat- 
ing cylinder.  The  essential  parts  then  are  as  follows :  — 

(i.)  A  pair  si  field-plates  A  and  B. 
(ii.)  A  set  of  rotating  carriers  p,  q,  r,  s,  t,  and  u. 
(iii.)  A  pair  of  neutralizing  brushes  n\,  nz,  made  of  flexible 
metal  wires,  the  function  of  which  is  to  touch  the 
carriers  while  they  are  under  the  influence  of  the 
field-plates.     They  are  connected   together  by  a 
diagonal  conductor,  which  need  not  be  insulated. 


FIG.  35.  —  Diagram  of  Typical  Influence  Machine. 


54  ELECTRICITY   AND   MAGNETISM        [PT.  i.  50 

(iv.)  A  pair  of  appropriating  brushes  ai}  a2,  which  reach 
over  from  the  field-plates  to  appropriate  the  charges 
that  are  conveyed  around  by  the  carriers,  and  im- 
part them  to  the  field-plates. 

(v.)  In  addition  to  the  above,  which  are  sufficient  to  con- 
stitute a  complete  self -exciting  machine,  it  is  usual 
to  add  a  discharging  apparatus,  consisting  of  two 
combs  Ci,  cz  to  collect  any  unappropriated  charges 
from  the  carriers  after  they  have  passed  the  appro- 
priating brushes ;  these  combs  being  connected  to 
the  adjustable  discharging  balls  at  D. 

The  operation  of  the  machine  is  as  follows.  The  neutral- 
izing brushes  are  set  so  as  to  touch  the  moving  carriers  just 
before  they  pass  out  of  the  influence  of  the  iield-plates. 
Suppose  the  field-plate  A  to  be  charged  ever  so  little  posi- 
tively, then  the  carrier  p,  touched  by  ni  just  as  it  passes, 
will  acquire  a  slight  negative  charge,  which  it  will  convey 
forward  to  the  appropriating  brush  ai}  and  will  thus  make  B 
slightly  negative.  Each  of  the  carriers  as  it  passes  to  the 
right  over  the  top  will  do  the  same  thing.  Similarly,  each  of 
the  carriers  as  it  passes  from  right  to  left  at  the  lower  side 
will  be  touched  by  n2  while  under  the  influence  of  the  — 
charge  on  B,  and  will  convey  a  small  +  charge  to  A  through 
the  appropriating  brush  «2.  In  this  way  A  will  rapidly  be- 
come more  and  more  +,  and  B  more  and  more  —  ;  and  the 
more  highly  charged  they  become,  the  more  do  the  collecting 
combs  Ci  and  c2  receive  of  unappropriated  charges.  Sparks 
will  snap  across  between  the  discharging  knobs  at  D. 

The  machine  will  not  be  self-exciting  unless  there  is  a 
good  metallic  contact  made  by  the  neutralizing  brushes 
and  by  the  appropriating  brushes.  If  the  discharging 
apparatus  were  fitted  at  Ci,  c2  with  contact  brushes  instead 
of  spiked  combs,  the  field-plates  of  the  machine  would  be 
liable  to  lose  their  charges,  or  even  to  have  the  charges  reversed 
in  sign,  whenever  a  large  spark  was  taken  from  the  knobs. 


CH.  i.  51]      TOEPLER'S    INFLUENCE   MACHINE  55 

It  will  be  noticed  that  there  are  two  thicknesses  of  glass 
between  the  fixed  field-plates  and  the  rotating  carriers.  The 
glass  serves  not  only  to  hold  the  metal  parts,  but  prevents 
the  possibility  of  back-discharges  (by  sparks  or  winds)  from 
the  carriers  to  the  field-plates  as  they  pass. 

The  essential  features  thus  set  forth  will  be  found  in 
Varley's  machine  of  1860,  in  Lord  Kelvin's  "  replenisher  " 
(which  had  only  two  carriers),  and  in  many  other  machines. 

51.  Toepler's  Influence  Machine.  —  In  this  machine,  as 
constructed  by  Voss,  are  embodied  various  points  due  to 
Holtz  and  others.  Its  construction  follows  almost  literally 


BACK   FIXED  DISK  WITH 
FIELD  PLATES  ON  BACK. 


FRONT  ROTATING   DISK 
WITH  CARRIERS  ON  FRONT. 


FIG.  30.  —  Toe^ler  (Voss)  Influence  Machine. 

the  diagram  already  explained,  but  instead  of  having  two 
cylinders,  one  inside  the  other,  it  has  two  flat  disks  of  var- 
nished glass,  one  fixed,  the  other  slightly  smaller  rotating  in 
front  of  it  (Fig.  36) .  The  field-plates  A  and  B  consist  of  pieces 
of  tinfoil,  cemented  on  the  back  of  the  back  disk,  each  protected 
by  a  coating  of  varnished  paper.  The  carriers  are  small  disks 
or  sectors  of  tinfoil,  to  the  number  of  six  or  eight,  cemented  to 
the  front  of  the  front  disk.  To  prevent  them  from  being  worn 
away  by  rubbing  against  the  brushes  a  small  metallic  button 
is  attached  to  the  middle  of  each.  The  neutralizing  brushes 
n\,  HZ,  are  small  whisps  of  fine  springy  brass  wire,  and  are 
mounted  on  the  ends  of  a  diagonal  conductor  Z.  The  appro- 


56  ELECTRICITY   AND   MAGNETISM         [PT.  i.  51 

priating  brushes  ai,  a2  are  also  of  thin  brass  wire,  and  are 
fastened  to  clamps  projecting  from  the  edge  of  the  fixed  disk, 
so  that  they  communicate  metallically  with  the  two  field- 
plates.  The  collecting  combs,  which  have  brass  spikes  so 
short  as  not  to  touch  the  carriers,  are  mounted  on  insulating 
pillars  and  are  connected  to  the  adjustable  discharging  knobs 
DI,  D2.  These  also  communicate  with  two  small  Leyden 
jars  Ji  J2,  the  function  of  which  is  to  accumulate  the  charges 
before  any  discharge  takes  place.  These  jars  are  separately 
depicted  in  Fig.  37.  Without  them,  the  discharges  between 
the  knobs  take  place  in  frequent  thin  blue  sparks.  With 
them  the  sparks  are  less  numerous,  but  very  brilliant  and 
noisy. 

To  use  the  Toepler  ( Voss)  machine  first  see  that  all  the  four 
brushes  are  so  set  as  to  make  good  metallic  contact  with  the 
carriers  as  they  move  past,  and  that  the  neutralizing  brushes 
are  set  so  as  to  touch  the  carriers  while  under  influence. 

Then  see  that  the  discharg- 
ing knobs  are  drawn  widely 
apart.  Set  the  machine  in 
rotation  briskly.  If  it  is 
clean  it  should  excite  itself 
after  a  couple  of  turns,  and 
will  emit  a  gentle  hissing 
.  ...•..;*:•.,::.;,.•:...;  .:  .:  .•:.  ...  .„.,.!.••..,.  ./.M.,..  '.  •  sound,  due  to  internal  dis- 

FIG.  37.  —  Leyden  Jars,  with  Spark  charges      (visible      as      blue 

Discharge-gap.  . 

glimmers  in  the  dark),  and 

will  offer  more  resistance  to  turning.  If  then  the  knobs  are 
pushed  nearer  together  sparks  will  pass  across  between  them. 
The  jars  should  be  kept  fre'e  from  dust.  Sometimes  a  pair  of 
terminal  screws  are  added  at  Si,  S2  (Fig.  37),  connected 
respectively  with  the  outer  coatings  of  the  jars.  These  are 
convenient  for  attaching  wires  to  lead  away  discharges  for 
experiments  at  a  distance.  If  not  so  used  they  should  be 
joined  together  by  a  short  wire,  as  the  two  jars  will  not 
work  properly  unless  their  outer  coatings  are  connected. 


CH.  i.  52]    WIMSHURST'S   INFLUENCE   MACHINE 


57 


52.  Wimshurst's  Influence  Machine.  —  In  this,  the  most 
widely  used  of  influence  machines,  there  are  no  fixed  field- 
plates.  In  its  simplest  form  it  consists  (Fig.  38)  of  two  circu- 
lar plates  of  varnished  glass,  which  are  geared  to  rotate  in 
opposite  directions.  A  number  of  sectors  of  metal  foil  are 
cemented  to  the  front  of  the  front  plate  and  to  the  back  of  the 
back  plate ;  these  sectors  serve  both  as  carriers  and  as  induc- 
tors. Across  the  front  is  fixed  an  uninsulated  diagonal  con- 
ductor, carrying  at  its  ends  neutralizing  brushes,  which  touch 


FIG.  38.  —  Wimshurst's  Influence  Machine. 

the  front  sectors  as  they  pass.  Across  the  back,  but  sloping 
the  other  way,  is  a  second  diagonal  conductor,  with  brushes 
that  touch  the  sectors  on  the  hinder  plate.  Nothing  more 
than  this  is  needed  for  the  machine  to  excite  itself  when  set 
in  rotation ;  but  for  convenience  there  is  added  a  collecting 
and  discharging  apparatus.  This  consists  of  two  pairs  of 
insulated  combs,  each  pair  having  its  spikes  turned  inwards 
toward  the  revolving  disks,  but  not  touching  them ;  one  pair 


58 


ELECTRICITY   AND   MAGNETISM         [PT.  i.  52 


being  on  the  right,  the  other  on  the  left,  mounted  each  on 
an  insulating  pillar  of  ebonite.  These  collectors  are  furnished 
with  a  pair  of  adjustable  discharging  knobs  overhead ;  and 
sometimes  a  pair  of  Leyden  jars  are  added,  to  prevent  the 
sparks  from  passing  until  considerable  quantities  of  charge 
have  been  collected. 

The  processes  that  occur  in  this  machine  are  best  explained 
by  aid  of  a  diagram  (Fig.  39) ,  in  which,  for  greater  clearness, 


FIG.  39.  —  Diagram  of  Wimshurst's  Influence  Machine. 

the  two  rotating  plates  are  represented  as  though  they  were 
two  cylinders  of  glass,  rotating  opposite  ways,  one  inside  the 
other.  The  inner  cylinder  will  represent  the  front  plate, 
the  outer  the  back  plate.  In  Figs.  38  and  39  the  front  plate 
rotates  right-handedly,  the  back  plate  left-handedly.  The 
neutralizing  brushes  r*i,  w2  touch  the  front  sectors,  while 
fts,  n4  touch  against  the  back  sectors. 

Now  suppose  any  one  of  the  back  sectors  represented 
near  the  top  of  the  diagram  to  receive  a  slight  positive  charge. 


CH.  i.  52]    WIMSHURST'S   INFLUENCE   MACHINE  59 

As  it  is  moved  onward  toward  the  left  it  will  come  opposite 
the  place  where  one  of  the  front  sectors  is  moving  past  the 
brush  HI.  The  result  will  be  that  the  sector  so  touched  while 
under  influence  by  HI  will  acquire  a  slight  negative  charge, 
which  it  will  carry  onwards  toward  the  right.  When  this 
negatively-charged  front  sector  arrives  at  a  point  opposite 
7*3  it  acts  inductively  on  the  back  sector  which  is  being 
touched  by  ns ;  hence  this  back  sector  will  in  turn  acquire  a 
positive  charge,  which  it  will  carry  over  to  the  left.  In  this 
way  all  the  sectors  will  become  more  and  more  highly  charged, 
the  front  sectors  carrying  over  negative  charges  from  left  to 
right,  and  the  back  sectors  carrying  over  positive  charges 
from  right  to  left.  At  the  lower  half  of  the  diagram  a  similar 
but  inverse  set  of  operations  will  be  taking  place.  For  when 
HI  touches  a  front  sector  under  the  influence  of  a  positive 
back  sector,  a  repelled  charge  will  travel  along  the  diagonal 
conductor  to  n2,  helping  to  charge  positively  the  sector  which 
it  touches.  The  front  sectors,  as  they  pass  from  right  to  left 
(in  the  lower  half) ,  will  carry  positive  charges,  while  the  back 
sectors,  after  touching  HI,  will  carry  negative  charges  from 
left  to  right.  The  metal  sectors  then  act  both  as  carriers 
and  as  inductors.  It  is  clear  that  there  will  be  a  continual 
carrying  of  positive  charges  toward  the  right,  and  of  nega- 
tive charges  to  the  left.  At  these  points,  toward  which 
the  opposite  kinds  of  charges  travel,  are  placed  the  col- 
lecting combs  communicating  with  the  discharging  knobs. 
The  latter  ought  to  be  opened  wide  apart  when  start- 
ing the  machine,  and  moved  together  after  it  has  excited 
itself. 

In  larger  Wimshurst  influence  machines  two,  three,  or 
more  pairs  of  oppositely-rotating  plates  are  mounted  within 
a  glass  case  to  keep  off  the  dust.  If  the  neutralizing  brushes 
make  good  metallic  contact  these  machines  are  all  self-ex- 
citing in  all  weathers.  Machines  with  only  six  or  eight 
sectors  on  each  plate  give  longer  sparks,  but  less  frequently 
than  those  that  have  a  greater  number.  Mr.  Wimshurst 


60  ELECTRICITY   AND   MAGNETISM         [PT.  i.  53 

designed  many  influence  machines,  from  small  ones  with  disks 
2  inches  across  up  to  that  at  South  Kensington,  which  has 
plates  7  feet  in  diameter. 

53.   Holtz's    Influence    Machine.  —  The    Holtz    machine 
in  its  typical  form  had  the  following  peculiarities.     There 
were  no  metal  carriers  upon  the 
rotating    plate,     hence    another 
mode  of  charging  it  had  to  be 
adopted  in  lieu  of  touching  con- 
ductors   while    under    influence, 
as  will  be  seen.     The  field-plates 
A  and  B  (Fig.  40)  were  of  var- 
nished paper  —  a  poor  conductor 
—  fastened  upon  the  back  of  the 
fixed  disk.     In  the  fixed  disk  of        FIG.  40.  —  Hoitz's  influence 
glass,   on  which  the  field-plates 

were  mounted,  there  were  cut  two  windows  or  openings, 
through  which  there  projected  from  the  field-plates  two 
pointed  paper  tongues,  which  took  the  place  of  appropriat- 
ing brushes.  The  discharging  knobs  were  inserted  in  the 
neutralizing  circuit  which  united  two  metal  combs  with 
pointed  spikes,  situated  in  front  of  the  rotating  front  disk, 
opposite  the  two  field-plates.  There  was  no  diagonal  con- 
ductor. Fig.  40  is  a  view  of  the  machine  from  behind.  The 
machine  was  not  self-exciting,  but  required  to  be  excited  by 
giving  it  a  small  initial  charge. 

The  action  of  the  machine  depends  upon  the  circum- 
stance that  the  surface  of  a  non-conducting  body  such  as 
glass  can  be  electrified  by  letting  off  against  it  an  electric 
wind  from  a  point  placed  near  it  (see  Art.  47). 

The  defects  of  the  Holtz  machine  were  that  it  was  so 
sensitive  to  damp  weather  as  to  be  unreliable,  that  it  was 
apt  suddenly  to  reverse  its  charges,  and  that  the  electric 
winds  by  which  it  operated  could  not  be  produced  with- 
out a  sufficiently  great  initial  charge.  Holtz  constructed 
many  forms  of  machine,  including  one  with  thirty-two 


CH.  i.  54,  55]  DISPERSAL   OF   FOG  61 

plates,  besides  machines  of  a  second  kind  having  two  glass 
plates  rotating  in  opposite  directions. 

54.  Experiments  with  Influence  Machines.  —  Every  kind 
of  influence  machine  is  reversible  in  its  action ;  that  is  to  say, 
that  if  a  continuous  supply  of  the  two  electricities  (furnished 
by  another  machine)  be  communicated  to  the  carriers,  the 
movable  plate  will  be  thereby  set  in  rotation  and,  if  allowed 
to  run  quite  freely,  will  run  as  a  motor,  turning  in  the  opposite 
direction  to  that  in  which  it  would  have  to  be  turned  in  order 
to  make  it  work  as  a  generator. 

Righi  showed  that  a  Holtz  machine  can  yield  a  continuous 
current  like  a  voltaic  battery,  the  strength  of  the  current 
being  nearly  proportional  to  the  velocity  of  rotation.  It  was 
found  that  the  electromotive-force  of  a  machine  was  equal 
to  that  of  52,000  Daniell's  cells,  or  nearly  53,000  volts, 
at  all  speeds.  The  resistance  when  the  machine  made 
120  revolutions  per  minute  was  2810  million  ohms;  but 
only  646  million  ohms  when  making  450  revolutions  per 
minute. 

The  experiments  described  in  Art.  46,  and  indeed  all 
those  usually  made  with  the  old  frictional  machines,  including 
the  charging  of  Ley  den  jars,  can  be  performed  by  the  aid  of 
influence  machines.  In  some  cases  it  is  well  to  connect  one 
of  the  two  discharging  knobs  to  the  earth  by  a  wire  or  chain, 
and  to  take  the  discharge  from  the  other  knob.  To  illumi- 
nate small  vacuum  tubes  they  may  be  connected  by  gutta- 
percha-covered  wires  to  the  two  discharging  knobs,  or  to  the 
terminals  Si,  S2  of  Fig.  37. 

55.  Dispersal  of  Fog.  —  The  electric  discharge   from   a 
point  possesses  the  curious  property  of  collecting  dust  or 
fumes  from  the  air.     This  is  readily  shown  by  connecting  one 
pole  of  an  influence  machine  by  a  wire  to  a  sharp-pointed 
needle  which  is  introduced  into  a  bell-jar  of  glass.     The 
latter  is  filled  with  fumes  by  burning  inside  it  a  bit  of  mag- 
nesium wire  or  brown  paper.     Then  on  turning  the  handle 
of  the  influence  machine  the  fumes  are  at  once  deposited, 


62  ELECTRICITY  AND   MAGNETISM        [PT.  i.  56 

and  the  air  left  clear.     Sir  Oliver  Lodge  has  proposed  this 
as  a  method  of  clearing  away  fogs. 


LESSON  VI.  —  The  Ley  den  Jar  and  other  Condensers 

56.  Action  across  a  Dielectric.  —  It  was  shown  in  previous 
lessons  that  the  opposite  charges  of  electricity  attract  one 
another;  that  electricity  cannot  flow  through  glass;  and 
that  yet  electricity  can  act  across  glass  by  influence.  Two 
suspended  pith-balls,  one  electrified  positively  and  the  other 
negatively,  will  attract  one  another  across  the  intervening 
air.  If  a  plate  of  glass  be  put  between  them  they  will  still 
attract  one  another,  though  neither  they  themselves  nor  the 
electric  charges  on  them  can  pass  through  the  glass.  If  a 
pith-ball  electrified  with  a  —  charge  be  hung  inside  a  dry 
glass  bottle,  and  a  rubbed  glass  rod  be  held  outside,  the  pith- 
ball  will  rush  to  the  side  of  the  bottle  nearest  to  the  glass 
rod,  being  attracted  by  the  +  charge  thus  brought  near  it. 
If  a  pane  of  glass  be  taken,  and  a  piece  of  tinfoil  be  stuck 
upon  the  middle  of  each  face  of  the  pane,  and  one  piece 
of  tinfoil  be  charged  positively,  and  the  other  negatively, 
the  two  charges  will  attract  one  another  across  the  glass, 
and  will  no  longer  be  found  to  be  free.  If  the  pane  is  set 
up  on  edge,  so  that  neither  piece  of  tinfoil  touches  the 
table,  it  will  be  found  that  hardly  any  electricity  can  be 
got  by  merely  touching  either  of  the  foils,  for  the  charges 
are  "  bound,  "  so  to  speak,  by  each  other's  attractions ; 
each  charge  is  inducing  the  other.  In  fact  it  will  be  found 
that  these  two  pieces  of  tinfoil  may  be,  in  this  manner, 
charged  a  great  deal  more  strongly  than  either  of  them  could 
possibly  be  if  it  were  stuck  to  a  piece  of  glass  alone,  and  then 
electrified.  In  other  words,  the  capacity  of  a  conductor  is 
greatly  increased  when  it  is  placed  near  to  a  conductor  electrified 
with  the  opposite  kind  of  charge.  If  its  capacity  is  increased, 
a  greater  quantity  of  electricity  may  be  put  into  it  before 
it  is  charged  to  an  equal  degree  of  potential.  Hence,  such 


CH.  i.  57] 


CONDENSERS 


63 


FIG.  41.  —  Condenser  made  of  two 
Metal  Plates. 


an  arrangement  for  holding  a  large  quantity  of  electrification 
may  be  called  a  condenser  of  electricity. 

57.  Condensers.  —  Next,  suppose  that  we  have  two 
brass  disks,  A  and  B  (Fig.  41),  set  upon  insulating  stems, 
and  that  a  glass  plate  is 
placed  between  them.  Let 
B  be  connected  by  a  wire 
to  the  knob  of  an  electrical 
machine,  and  let  A  be  joined 
by  a  wire  to  "  earth."  The 
H-  charge  upon  B  will  act 
inductively  across  the  glass 
plate  on  A,  and  will  draw 
electrons  out  of  the  earth,  making  the  nearest  face  of  A 
negatively  electrified.  This  —  charge  on  A  will  attract 
the  +  charge  of  B  to  the  side  nearest  the  glass,  and  a  fresh 
supply  of  electricity  will  come  from  the  machine.  Thus 
this  arrangement  will  become  a  condenser.  If  the  two 
brass  disks  are  pushed  up  close  to  the  glass  plate  there  will 
be  a  still  stronger  attraction  between  the  +  and  —  charges, 
because  they  are  now  nearer  one  another,  and  the  inductive 
action  will  be  greater;  hence  a  still  larger  quantity  can  be 
accumulated  in  the  plates.  We  see  then  that  the  capacity 
of  a  condenser  is  increased  by  bringing  the  plates  near  to- 
gether. If  now,  while  the  disks  are  strongly  charged,  the 
wires  are  removed  and  the  disks  are  drawn  backwards  from 
one  another,  the  two  charges  will  not  hold  one  another 
bound  so  strongly,  and  there  will  be  more  free  electrification 
than  before  over  their  surfaces.  This  would  be  rendered 
evident  to  the  experimenter  by  the  little  pith-ball  electro- 
scopes fixed  to  them  (see  the  Fig.),  which  would  fly  out  as  the 
brass  disks  were  moved  apart.  We  have  put  no  further  charge 
on  the  disk  B,  and  yet,  from  the  indications  of  the  electroscope, 
we  should  conclude  that  by  moving  it  away  from  disk  A 
it  has  become  electrified  to  a  higher  degree.  The  fact  is, 
that  while  the  conductor  B  was  near  the  -  charge  of  A 


64  ELECTRICITY   AND   MAGNETISM        [PT.  i.  58 

the  capacity  of  B  was  greatly  increased,  but  on  moving  it 
away  from  A  its  capacity  has  diminished,  and  hence  the 
same  quantity  of  electricity  now  electrifies  it  to  a  higher 
degree  than  before.  The  presence,  therefore,  of  an  earth- 
connected  plate  near  an  insulated  conductor  increases  its 
capacity,  and  permits  it  to  accumulate  a  greater  charge  by 
attracting  and  condensing  the  electricity  upon  the  face 
nearest  the  earth-plate,  the  surface-density  on  this  face 
being  therefore  very  great ;  hence  the  appropriateness  of 
the  term  condenser  as  applied  to  the  arrangement.  It  was 
formerly  also  called  an  accumulator ;  but  the  term  accumu- 
lator is  now  reserved  for  the  special  kind  of  battery  for  storing 
the  energy  of  electric  currents  (Art.  572). 

The  stratum  of  air  between  the  two  disks  will  suffice 
to  insulate  the  two  charges  one  from  the  other.  The 
brass  disks  thus  separated  by  a  stratum  of  air  constitute 
an  air-condenser,  or  air-leyden.  Such  condensers  were  first 
devised  by  Wilcke  and  Aepinus.  In  these  experiments  the 
sheet  of  glass  or  layer  of  air  acts  as  a  dielectric  (Art.  315) 
conveying  the  inductive  action  through  its  substance.  All 
dielectrics  are  insulators,  but  equally  good  insulators  are  not 
necessarily  equally  good  dielectrics.  Air  and  glass  are  far 
better  insulators  than  ebonite  or  paraffin  in  the  sense  of  being 
much  worse  conductors.  But  influence  acts  more  strongly 
across  a  slab  of  glass  than  across  a  slab  of  ebonite  or  paraffin 
of  equal  thickness,  and  better  still  across  these  than  across  a 
layer  of  air.  In  other  words,  glass  is  a  better  dielectric  than 
ebonite,  or  paraffin,  or  air,  as  it  possesses  a  higher  inductive 
capacity. 

It  will  then  be  seen  that  in  the  act  of  charging  a  condenser, 
as  much  electricity  flows  out  at  one  side  as  flows  in  at  the 
other. 

58.  Displacement.  —  Whenever  electric  forces  act  on  a 
dielectric,  tending  to  drive  electricity  in  at  one  side  and 
out  at  the  other,  we  may  draw  lines  of  force  through  the 
dielectric  in  the  direction  of  the  action,  and  we  may  consider 


CH.  i.  59,  60]  THE    LEYDEN  JAR  65 

tubular  spaces  mapped  out  by  such  lines.  We  may  consider 
a  tube  of  electric  force  having  at  one  end  a  definite  area 
of  the  positively  charged  surface,  and  at  the  other  end  an 
area  of  the  negatively  charged  surface.  These  areas  may  be 
of  different  size  or  shape,  but  the  quantities  of  +  and  — 
electrification  over  them  will  be  equal.  The  quantity  of 
electricity  which  has  apparently  been  transferred  along  the 
tube  was  called  by  Maxwell  "  the  displacement"  In  non- 
conductors it  is  proportional  to  the  electromotive-force.  In 
conductors  electromotive  forces  produce  currents,  which 
may  be  regarded  as  displacements  that  increase  continuously 
with  time.  In  certain  crystalline  media  the  displacement 
does  not  take  place  exactly  in  the  direction  of  the  electric 
force :  in  this  case  we  should  speak  of  tubes  of  influence 
rather  than  tubes  of  force.  A  unit  tube  will  be  bounded  at  its 
two  ends  by  unit  charges  -f-  and  — .  We  may  consider  the 
whole  electric  field  between  positively  and  negatively  charged 
bodies  as  mapped  out  into  such  tubes. 

59.  Capacity    of   a   Condenser.  —  It   appears,    therefore, 
that  the  capacity  of  a  condenser  will  depend  upon  — 

(1)  The  size  and  form  of  the  metal  plates  or  coatings. 

(2)  The  thinness  of  the  stratum  of  dielectric  between 

them ;  and 

(3)  The  dielectric  capacity  of  the  material. 

60.  The    Leyden    Jar.  —  The   Leyden   Jar,    called   after 
the  city  where  it  was  invented,  is  a  convenient  form  of 
condenser.     It  usually  consists  (Fig. 

42)  of  a  glass  jar  coated  up  to  a  cer- 
tain height  on  the  inside  and  out- 
side with  tinfoil.  A  brass  knob  fixed 
on  the  end  of  a  stout  brass  wire  passes 
downward  through  a  lid  or  top  of 
dry  well-varnished  wood,  and  com- 
municates by  a  loose  bit  of  brass 
chain  with  the  inner  coating  of  foil.  FIG.  42.  —  Leyden  jar. 


66  ELECTRICITY  AND   MAGNETISM        [PT.  i.  61 

To  charge  the  jar  the  knob  is  held  to  the  prime  conduc- 
tor of  an  electrical  machine,  the  outer  coating  being  either 
held  in  the  hand  or  connected  to  "  earth  "  by  a  wire  or 
chain.  When  a  +  charge  of  electricity  is  imparted  thus  to 
the  inner  coating,  it  acts  inductively  on  the  outer  coating, 
attracting  a  —  charge  into  the  face  of  the  outer  coating 
nearest  the  glass,  and  repelling  a  +  charge  to  the  out- 
side of  the  outer  coating,  and  thence  through  the  hand  or 
wire  to  earth.  After  a  few  moments  the  jar  will  have  acquired 
its  full  charge,  the  outer  coating  being  —  and  the  inner  +. 
If  the  jar  is  of  good  glass,  and  dry,  and  free 
from  dust,  it  will  retain  its  charge  for  many 
hours  or  days.  But  if  a  path  be  provided 
by  which  the  two  mutually  attracting  elec- 
tricities can  flow  to  one  another,  they  will 
do  so,  and  the  jar  will  be  instantaneously 
discharged.  If  the  outer  coating  be  grasped 
with  one  hand,  and  the  knuckle  of  the  other 
hand  be  presented  to  the  knob  of  the  jar, 
FIG.  43.  —  Discharg-  a  bright  spark  will  pass  between  the  knob 
and  the  knuckle  with  a  sharp  report,  and 
at  the  same  moment  a  convulsive  "  shock  "  will  be  com- 
municated to  the  muscles  of  the  wrists,  elbows,  and  shoulders. 
A  safer  means  of  discharging  the  jar  is  afforded  by  the  dis- 
charging tongs  or  discharger  (Fig.  43),  which  consists  of  a 
jointed  brass  rod  provided  with  brass  knobs  and  a  glass 
handle.  One  knob  is  laid  against  the  outer  coating,  the  other 
is  then  brought  near  the  knob  of  the  jar,  and  a  bright  snap- 
ping spark  leaping  from  knob  to  knob  announces  that  the 
two  accumulated  charges  have  flowed  together,  completing 
the  discharge.  Sometimes  a  jar  discharges  itself  by  a  spark 
climbing  over  the  top  edge  of  the  jar.  Often  when  a  jar  is 
well  charged  a  hissing  sound  is  heard,  due  to  partial  discharges 
creeping  over  the  edge.  They  can  be  seen  in  the  dark  as  pale 
phosphorescent  streams. 

61.    Discovery  of  the  Leyden  Jar.  —  The  discovery  of  the 


CH.  i.  62,  63]  LEYDEN   JARS  67 

Ley  den  jar  arose  from  the  attempt  of  Musschenbroek  and 
his  pupil  Cuneus  l  to  collect  the  supposed  electric  "  fluid  " 
in  a  bottle  half  rilled  with  water,  which  was  held  in  the  hand 
and  was  provided  with  a  nail  to  lead  the  "  fluid  "  down 
through  the  cork  to  the  water  from  the  electric  machine. 
Here  the  water  served  as  an  inner  coating  and  the  hand  as 
an  outer  coating  to  the  jar.  Cuneus  on  touching  the  nail 
received  a  shock.  This  accidental  discovery  created  the 
greatest  excitement  in  Europe  and  America. 

62.  Residual  Charges.  —  If  a  Leyden  jar  be  charged  and 
discharged  and  then  left  for  a  little  time  to  itself,  it  will 
be  found  on  again  discharging  that  a  small  second  spark 
can  be  obtained.     There  is  in  fact  a  residual  charge  which 
seems  to  have  soaked  into  the  glass  or  been  absorbed.     The 
return  of  the  residual  charge  is  hastened  by  tapping  the  jar. 
The  amount  of  the  residual  charge  varies  with  the  time  that 
the  jar  has  been  left  charged  ;  it  also  depends  on  the  kind  of 
glass  of  which  the  jar  is  made.     There  is  no  residual  charge 
discoverable  in  an  air-leyden  after  it  has  once  been  dis- 
charged. 

63.  Batteries  of  Leyden  Jars.  —  A  large  Leyden  jar  will 
give  a  more  powerful  shock  than  a  small  one,  for  a  larger 
charge  can  be  put  into  it ;    its  capacity  is  greater.     If  it  is 
desired  to  accumulate  a  very  great  charge  of  electricity,  a 
number  of  jars  must  be  employed,  all  their  inner  coatings 
being  connected  together,  and  all  their  outer  coatings  being 
united.     This  arrangement  is  called  a  battery  of  Leyden  jars, 
or  Leyden  battery  (Fig.  44).     As  it  has  a  large  capacity,  it 
will  require  a  large  quantity  of  electricity  to  charge  it  fully. 
When  charged  it  produces  very  powerful  effects ;    its  spark 
will  pierce  glass  readily,  and  every  care  must  be  taken  to 
avoid  a  shock  from  it  passing  through  the  person,  as  it  might 
be  fatal.     A  Leyden  jar  made  of  thin  glass  has  a  greater 
capacity  as  a  condenser  than  a  thick  one  of  the  same  size; 

1  The  honour  of  the  invention  of  the  jar  is  also  claimed  for  Kleist,  Bishop 
of  Pomerania. 


68  ELECTRICITY   AND   MAGNETISM        [PT.  i.  64 

but  if  it  is  too  thin  it  will  be  destroyed  when  powerfully 
charged  by  a  spark  actually  piercing  the  glass.  To  prevent 
jars  from  being  pierced  by  a  spark,  the  highest  part  of  the 


FIG.  44.  —  Battery  of  Leyden  Jars. 

inside  coating  should  be  connected  across  by  a  strip  of  foil 
or  a  metallic  disk  to  the  central  wire. 

64.  High  Voltage  Jars.  —  If  a  jar  is  desired  to  give  long 
sparks,  there  must  be  left  a  long  space  of  varnished  glass 
above  the  top  of  the  coatings. 

For  use  in  wireless  telegraphy,  with  very  high  voltages, 
special  jars  are  used,  of  a  pattern  due  to  Moscicki,  consisting 
of  a  long  cylindrical  tube  of  glass,  Fig.  45,  on  the  outside 
and  inside  of  which  films  of  copper  have  been  deposited  ; 
the  glass  tube  being  specially  thickened  at  the  upper  end 
to  prevent  piercing  by  a  spark  at  the  top  edges  of  the  metal 
coatings. 

For  the  forms  of  condensers  used  in  telegraphy  see  Art. 
322,  p.  281. 


CH.  i.  65,  66] 


DIELECTRIC    STRAIN 


69 


65.  Seat  of  the  Charge.  —  Benjamin  Franklin  discovered 
that  the  charges  of  the  Ley  den  jar  really  reside  on  the  surface 
of  the  glass,  not  on  the  metallic  coatings.  This  he 
proved  by  means  of  a  jar  whose  coatings  could  be 
removed  (Fig.  46).  The  jar  was  charged  and  placed 
upon  an  insulating  stand.  The 
inner  coating  was  then  lifted  out, 
and  the  glass  jar  was  then  taken 
out  of  the  outer  coating.  Neither 
coating  was  found  to  be  electri- 
fied to  any  extent,  but  on  again 
putting  the  jar  together  it  was 
found  to  be  highly  charged.  The 
charges  had  all  the  time  remained 
upon  the  inner  and  outer  sur- 
faces of  the  glass  dielectric. 

66.  Dielectric  Strain.  —  Fara- 
day proved  that  the  medium 
across  which  influence  takes  place 
really  plays  an  important  part 
in  the  phenomena.  It  is  now 
known  that  all  dielectrics  across 
which  inductive  actions  are  at 
work  are  thereby  strained.1  Inasmuch  as  a  good  vacuum  is 
a  good  dielectric,  it  is  clear  that  it  is  not  necessarily  the 
material  particles  of  the  dielectric  substance  that  are  thus 
affected ;  hence  it  is  believed  that  electrical  phenomena  are 
due  to  stresses  and  strains  in  the  so-called  "  ether  "  (the  thin 
medium  pervading  all  matter  and  all  space),  the  highly  elastic 
constitution  of  which  enables  it  to  convey  to  us  the  vibrations 
of  light,  though  it  is  millions  of  times  less  dense  than  air.  As 
the  particles  of  bodies  are  intimately  surrounded  by  ether,  the 
stresses  in  the  ether  are  also  communicated  to  the  particles  of 

1  In  the  exact  sciences  a  strain  means  an  alteration  of  form  or  volume 
due  to  the  application  of  a  stress.  A  stress  is  the  force,  pressure,  or  other 
agency  which  produces  a  strain. 


FIG.  45.  — 
Moscicki 
Leyden 
Jar. 


FIG.  46.  —  Dissectable 
Leyden  Jar. 


70  ELECTRICITY   AND   MAGNETISM        [PT.  i.  67 

bodies,  and  they  too  suffer  a  strain.  The  glass  between  the 
two  coatings  of  tinfoil  in  the  Leyden  jar  is  actually  strained 
or  squeezed,  there  being  a  tension  along  the  lines  of  electric 
force.  When  an  insulated  charged  ball  is  hung  up  in  a  room 
an  equal  amount  of  the  opposite  kind  of  charge  is  attracted 
to  the  inside  of  the  walls,  and  the  air  between  the  ball  and  the 
walls  is  strained  (electrically)  like  the  glass  of  the  Leyden  jar. 
If  a  Leyden  jar  is  made  of  thin  glass  it  may  give  way  under 
the  stress;  and  when  a  Leyden  jar  is  discharged  the  layer 
of  air  between  the  knob  of  the  jar  and  the  knob  of  the  dis- 
charging tongs  is  more  and  more  strained  as  they  are  ap- 
proached towards  one  another,  till  at  last  the  stress  becomes 
too  great,  and  the  layer  of  air  gives  way,  and  is  perforated 
by  the  spark  that  discharges  itself  across.  The  existence  of 
such  stresses  enables  us  to  understand  the  residual  charge  of 
Leyden  jars  in  which  the  glass  does  not  recover  itself  all  at 
once,  by  reason  of  its  viscosity,  from  the  strain  to  which  it 
has  been  subjected.  It  must  never  be  forgotten  that  electric 
force  acts  across  space  in  consequence  of  the  transmission 
of  stresses  and  strains  in  the  medium  with  which  space  is 
filled.  In  every  case  we  store  not  electricity  but  energy. 
Work  is  done  in  pushing  electricity  from  one  place  to  another 
against  the  forces  which  tend  to  oppose  the  movement. 
The  charging  of  a  Leyden  jar  may  be  likened  to  the  operation 
of  bending  a  spring,  or  to  pumping  up  water  from  a  low  level 
to  a  high  one.  In  charging  a  jar  we  pump  exactly  as  many 
electrons  into  the  negative  side  as  we  pump  out  of  the  positive 
side,  and  we  spend  energy  in  so  doing.  It  is  this  stored  en- 
ergy which  afterwards  reappears  in  the  discharge. 

LESSON  VII.  —  Other  Sources  of  Electrification 

67.  Other  Sources.  —  It  was  remarked  at  the  close  of 
Lesson  I.  (p.  12)  that  friction  was  by  no  means  the  only 
means  of  electrification.  Some  of  the  other  sources  will  now 
be  named. 


CH.  i.  68-72]    SOURCES   OF   ELECTRIFICATION  71 

68.  Percussion.  —  A  violent  blow  struck  by  one  substance 
upon  another  produces  opposite  electrical  states  on  the  two 
surfaces.     It  is  possible  indeed  to  draw  up  a  list  resembling 
that  of  Art.  7,  in  such  an  order  that  each  substance  will  take 
a  +  charge  on  being  struck  with  one  lower  on  the  list. 

69.  Disruption  and  Cleavage.  —  If  a  card  be  torn  asunder 
in  the  dark,  sparks  are  seen,  and  the  separated  portions, 
when  tested  with  an  electroscope,  will  be  found  to  be  elec- 
trical.    The  linen  faced  with  paper  used  in  making  strong 
envelopes  and  for  paper  collars,  shows  this  very  well.     Lumps 
of  sugar,  crunched  in  the  dark  between  the  teeth,  exhibit  pale 
flashes  of  light.     The  sudden  cleavage  of  a  sheet  of  mica 
also  produces  sparks,  and  both  laminae  are  found  to  be  elec- 
trified. 

70.  Crystallization  and  Solidification.  —  Many  substances, 
after  passing  from  the  liquid  to  the  solid  state,  exhibit  elec- 
trical conditions.     Sulphur  fused  in  a  glass  dish  and  allowed 
to  cool  is  violently  electrified,  as  may  be  seen  by  lifting  out 
the  crystalline  mass  with  a  glass  rod.     Chocolate  also  becomes 
electrical  during  solidification.     When  arsenic  acid  crystal- 
lizes out  from  its  solution  in  hydrochloric  acid,  the  formation 
of  each  crystal  is  accompanied  by  a  flash  of  light,  doubtless 
due  to  an  electrical  discharge.     A  curious  case  occurs  when 
the  sulphate  of  copper  and  potassium  is  fused  in  a  crucible. 
It  solidifies  without  becoming  electrical,  but  on  cooling  a 
little  further  the  crystalline  mass  begins  to  fly  to  powder 
with  an  instant  evolution  of  electricity. 

71.  Combustion.  —  Volta  showed  that  combustion  gen- 
erated electricity.     A  piece  of  burning  charcoal,  or  a  burn- 
ing pastille,  such  as  is  used  for  fumigation,  placed  in  connexion 
with  the  knob  of  a  gold-leaf  electroscope,  will  cause  the  leaves 
to  diverge. 

72.  Evaporation.  —  The  evaporation  of  liquids  is  often 
accompanied  by  electrification,  the  liquid  and  the  vapour 
assuming  opposite  states,  though  apparently  only  when  the 
surface  is  in  agitation.     A  few  drops  of  a  solution  of  sulphate 


72  ELECTRICITY  AND   MAGNETISM     [PT.  i.  73-75 

of  copper  thrown  into  a  hot  platinum  crucible  produce  violent 
electrification  as  they  evaporate. 

73.  Atmospheric  Electricity.  —  The  atmosphere  is  found 
to  be  always  electrified  relatively  to  the  earth  :  this  is  due,  in 
part  possibly,  to  evaporation  going  on  over  the  oceans.     The 
subject  of  atmospheric  electricity  is  treated   of  separately 
in  Arts.  353  to  361. 

74.  Compression.  —  A  large  number  of  substances  when 
compressed  exhibit  electrification  on  their  surface.     Thus 
cork  becomes  +  when  pressed  against  amber,  guttapercha, 
and  metals  ;  while  it  takes  a  —  charge  when  pressed  against 
spars  and  animal  substances. 

75.  Pyro-electricity.  —  There  are  certain  crystals  which, 
while  being  heated  or  cooled,  exhibit  electrical  charges  at 
certain  regions  or  poles.     Crystals  thus  electrified  by  heating 
or  cooling  are  said  to  be  pyro-electric.     Chief  of  these  is  the 
Tourmaline,  whose  power  of  attracting  light  bodies  to  its 
ends  after  being  heated  has  been  known  for  some  centuries. 
It  is  alluded  to  by  Theophrastus  and  Pliny  under  the  name 
of  Lapis  Lyncurius.     Tourmaline  is  a  hard  mineral,  semi- 
transparent  when  cut  into  thin  slices,  and  of  a  dark  green  or 
brown  colour,  but  looking  perfectly  black  and  opaque  in  its 
natural  condition,  and  possessing  the  power  of  polarizing  light. 
It  is  usually  found  in  slightly  irregular  three-sided  prisms 
which,  when  perfect,  are  pointed  at  both  ends.     It  belongs 
to  the  "  hexagonal  system  of  crystals,  but  is  only  hemihedral, 
that  is  to  say,  has  the  alternate  faces  only  developed.     Its 
form  is  given  in  Fig.  47,  where  a  general  view  is  first  shown, 
the  two  ends  A  and  B  being  depicted  in  separate  plans. 
These  two  ends  differ  slightly  in  shape.     Each  is  made  up 
of  three  sloping  faces  terminating  in  a  point.     But  at  A  the 
edges  between  these  faces  run  down  to  the  corners  of  the 
prism,  while  in  B  the  edges  between  the  terminal  faces  run 
down  to  the  middle  points  of  the  long  faces  of  the  prism. 
The  end  A  is  known  as  the  analogous  pole,  and  B  as  the  an- 
tilogous pole.     While  the  crystal  is  rising  in  temperature  A 


CH.'I.  75] 


PYRO-ELECTRIC   CRYSTALS 


73 


exhibits  +  electrification,  B  —  ;  but  if,  after  having  been 
heated,  it  is  allowed  to  cool,  the  polarity  is  reversed;  for 
during  the  time  that  the  temperature  is  falling  B  is  -f  and  A 
is  — .  If  the  temperature  is  steady  no  such  electrical  effects 
are  observed  either  at  high  or  low  temperatures;  and  the 
phenomena  cease  if  the  crystal  be  warmed  above  150°  C. 
This  is  not,  however,  due  to  the  crystal  becoming  a  conductor 
at  that  temperature ;  for  its  resistance  at  even  higher  tem- 
peratures is  still  so  great  as  to  make  it  practically  a  non- 
conductor. A  heated  crystal  of  tourmaline  suspended  by  a 
silk  fibre  may  be  attracted  and  repelled  by  electrified  bodies, 


M/ 


^^\~/*v^ 

^ 

-T-^& 

p 

Too 

0'° 

A; 

—t  [ 

W" 

FIG.  47.  —  Crystal  of  Tourmaline. 


FIG.  48.  —  Crystal  of  Boracite. 


or  by  a  second  heated  tourmaline ;  the  two  similar  poles  re- 
pelling one  another,  while  the  two  poles  of  opposite  form 
attract  one  another.  If  a  crystal  be  broken  up,  each  fragment 
is  found  to  possess  also  an  analogous  and  an  antilogous  pole. 
Many  other  crystals  beside  the  tourmaline  are  more  or 
less  pyro-electric.  Amongst  these  are  silicate  of  zinc  ("elec- 
tric calamine  "),  boracite,  cane-sugar,  quartz,  tartrate  of 
potash,  sulphate  of  quinine,  and  several  others.  Boracite 
crystallizes  in  the  form  shown  in  Fig.  48,  which  represents 
a  cube  having  four  alternate  corners  truncated.  The  cor- 
ners not  truncated  behave  as  analogous  poles,  the  truncated 
ones  as  antilogous.  When  a  natural  hexagonal  prism  of 
quartz  is  heated  its  six  edges  are  found  to  be  +  and  —  in 
alternate  order. 


74  ELECTRICITY   AND   MAGNETISM   [PT.  i.  76,  7/ 

76.  Piezo-electricity.  —  In  certain  crystals  pressure  in  a 
particular  direction  may  produce  electrification.  Haiiy 
found  that  a  crystal  of  calcspar  pressed  between  the  dry 
fingers,  so  as  to  compress  it  along  the  blunt  edges  of  the 
crystal,  became  electrical,  and  that  it  retained  its  electricity 
for  some  days.  He  even  proposed  to  employ  a  squeezed 
suspended  crystal  as  an  electroscope.  A  similar  property 
is  alleged  of  mica,  topaz,  and  fluorspar.  If  two  opposite 
edges  of  a  hexagonal  prism  of  quartz  are  pressed  together, 

one  becomes  +,  the  other  — .  Pres- 
sure also  produces  opposite  kinds  of 
electrification  at  opposite  ends  of  a 
crystal  of  tourmaline,  and  of  other 
crystals  of  the  class  already  noticed 
as  possessing  the  peculiarity  of  skew- 
symmetry  or  hemihedry  in  their 
structure.  Piezo-electricity  is  the 
name  given  to  this  branch  of  the 
science.  It  is  known  that  skew- 
symmetry  of  structure  is  dependent 
on  molecular  constitution ;  and  it 
is  doubtless  the  same  peculiarity 
which  determines  the  pyro-electric 
and  piezo-electric  properties,  as  well 
as  the  optical  behaviour  of  these 
crystals  in  polarized  light. 

77.  Animal  Electricity.  —  Several 
species  of  creatures  inhabiting  the 
water  have  the  power  of  producing 

FIG.  49. -Torpedo  or  Raia.          ^^     dischargeg     physiologically. 

The  best  known  of  these  creatures  are  the   Torpedo,  the 
Gymnotus,  and  the  Silurus.     The  Raia  Torpedo,1  or  electric 

1  It  is  a  curious  point  that  the  Arabian  name  for  the  torpedo,  ra-ad,  signifies 
lightning.  This  is  perhaps  not  so  curious  as  that  the  Electro,  of  the  Homeric 
legends  should  possess  certain  qualities  that  would  tend  to  suggest  that  she 
is  a  personification  of  the  lightning.  The  resemblance  between  the  names 
electra  and  electron  (amber)  cannot  be  accidental. 


CH.  i.  78-80]  CONTACT    OF    DISSIMILAR    METALS  75 

ray,  of  which  there  are  three  species  inhabiting  the  Medi- 
terranean and  Atlantic,  is  provided  with  an  electric  organ  on 
the  back  of  its  head  as  shown  in  Fig.  49.  This  organ  consists 
of  laminae  composed  of  polygonal  cells  to  the  number  of  800 
or  1000,  or  more,  sup- 
plied with  four  large 
bundles  of  nerve  fi- 
bres ;  the  under  sur- 
face of  the  fish  is  — , 
the  upper +.  In  the 

/-,  ,       ,    .  FIG.  50.  —  Electric  Eel  or  Gymnotus. 

Gymnotus  electricus, 

or  Surinam  eel  (Fig.  50),  the  electric  organ  goes  the  whole 
length  of  the  body  from  tail  to  head.  Humboldt  gives  a 
lively  account  of  the  combats  between  the  electric  eels  and 
the  wild  horses,  driven  by  the  natives  into  the  swamps  in- 
habited by  the  Gymnotus.  It  is  able  to  give  a  most  terrible 
shock,  and  is  a  formidable  antagonist  when  it  has  attained 
its  full  length  of  5  or  6  feet.  In  the  Silurus  the  current  flows 
from  head  to  tail. 

Nobili,  Matteucci,  and  others  have  shown  that  nerve- 
excitations  and  muscular  contractions  of  human  beings 
also  give  rise  to  feeble  discharges  of  electricity.  The 
beating  of  the  heart  creates  a  rhythmical  electromotive 
force. 

78.  Electricity  of  Vegetables.  —  Buff  thought  he  detected 
electrification  produced  by  plant  life;    the  roots  and  juicy 
parts  being  negatively,  and  the  leaves  positively,  electrified. 
The  subject  has,  however,  been  little  investigated. 

79.  Thermo-electricity.  —  Heat  applied   at   the  junction 
of  two  dissimilar  metals  produces  a  flow  of  electricity  across 
the  junction.     This  subject  is  discussed  in  Arts.  471  to  480 
on  Thermo-electric  Currents. 

80.  Contact  of  Dissimilar  Metals.  —  Volta  showed  that 
the  contact  of  two  dissimilar  metals  in  air  produced  opposite 
kinds  of  electrification,  one  t becoming  positively,  and  the 
other  negatively,   electrified.     This  he  proved  in  several 


76 


ELECTICITY   AND   MAGNETISM         [PT.  i.  80 


ways,  one  of  the  most  conclusive  proofs  being  that  afforded 
by  his  condensing  electroscope.  This  consisted  of  a  gold-leaf 
electroscope  combined  with  a  small  condenser.  A  metallic 
plate  formed  the  top  of  the  electroscope,  and  on  this  was 
placed  a  second  metallic  plate  furnished  with  a  handle,  and 

insulated  from  the  lower  one 
by  being  well  varnished  at  the 
surface  (Fig.  51).  As  the 
capacity  of  such  a  condenser 
is  considerable,  a  very  feeble 
source  may  supply  a  quantity 
of  electricity  to  the  condenser 
without  materially  raising  its 
potential,  or  causing  the  gold 
leaves  to  diverge.  But  if  the 
upper  plate  be  lifted,  the  ca- 
pacity of  the  lower  plate  di- 
minishes enormously,  and  the 
potential  of  its  charge  rises 
as  shown  by  the  divergence 
of  the  gold  leaves.1  To  prove 
by  the  condensing  electro- 
scope that  contact  of  dissimilar  metals  does  produce  elec- 
trification, a  small  compound  bar  made  of  two  dissimilar 
metals  —  say  zinc  and  copper  —  soldered  together,  is  held 
in  the  moist  hand,  and  one  end  of  it  is  touched  against  the 
lower  plate,  the  upper  plate  being  placed  in  contact  with  the 
ground  or  touched  with  the  finger.  When  the  two  opposing 
charges  have  thus  collected  in  the  condenser  the  upper  plate 
is  removed,  and  the  diverging  of  the  gold  leaves  shows  the 

1  Formerly,  this  action  was  accounted  for  by  saying  that  the  electricity, 
which  was  "bound"  when  the  plates  of  the  condenser  were  close  together, 
becomes  "free"  when  the  top  plate  is  lifted  up;  the  above  is,  however,  a 
more  scientific  and  more  accurate  way  of  saying  the  same  thing.  The 
student  who  is  unable  to  reconcile  these  two  ways  of  stating  the  matter 
should  read  again  Articles  41  and  56,  on  pp.  43  and  62.  A  much  more  sensi- 
tive apparatus  to  show  the  effect  is  the  quadrant  electrometer  (Art.  307). 


FIG.  51.  —  Experiment  showing  Electri- 
fication by  Contact. 


CH.  i.  81]        ELECTRIFICATION   BY   CONTACT  77 

presence  of  a  free  charge,  which  can  afterwards  be  examined 
to  see  whether  it  be  +  or  — .  Instead  of  employing  the  cop- 
per-zinc bar,  a  single  voltaic  cell  may  be  connected  by  copper 
wires  to  the  two  plates.  For  a  long  time  the  existence  of 
this  electrification  by  contact  was  denied,  or  rather  it  was  de- 
clared to  be  due  (when  occurring  in  voltaic  combinations 
such  as  are  described  in  Lesson  XIII.)  to 
chemical  actions  going  on ;  whereas  the 
real  truth  is  that  the  electricity  of  contact 
and  the  chemical  action  are  both  due  to 
transfers  of  electrons  between  the  sub- 
stances under  the  actions  of  forces  about 
FIG.  52.  —  Kelvin's  Proof  which  very  little  is  known  with  certainty. 

of  Contact  Electricity.  J 

Later  experiments,  especially  those  made 
with  the  modern  delicate  electrometers  of  Lord  Kelvin,  put 
beyond  doubt  the  reality  of  Volta's  discovery.  One  simple 
experiment  explains  the  method  adopted.  A  thin  strip  or 
needle  of  metal  is  suspended  so  as  to  turn  about  a  point  C. 
It  is  electrified  from  a  known  source.  Under  it  are  placed 
(Fig.  52)  two  semicircular  disks,  or  half-rings  of  dissimilar 
metals.  Neither  attracts  or  repels  the  electrified  needle 
until  the  two  are  brought  into  contact,  or  connected  by 
a  third  piece  of  metal,  when  the  needle  immediately  turns, 
being  attracted  by  the  one  that  is  oppositely  electrified, 
and  repelled  by  the  one  that  is  electrified  similarly  with 
itself. 

81.  Contact  Series  of  Metals  (in  Air).  — Volta  found, 
moreover,  that  the  differences  of  electric  potential  between 
the  different  pairs  of  metals  were  not  all  equal.  Thus,  while 
zinc  and  lead  were  respectively  +  and  —  to  a  slight  degree, 
he  found  zinc  and  silver  to  be  respectively  +  and  —  to  a  much 
greater  degree.  He  was  able  to  arrange  the  metals  in  a  series 
such  that  each  one  enumerated  became  positively  electrified 
when  placed  in  contact  in  air  with  one  below  it  in  the  series. 
Those  in  italics  are  added  from  observations  made  since 
Volta's  time  — 


78  ELECTRICITY   AND   MAGNETISM         [PT.  i.  81 

+  Sodium,  Iron, 

Magnesium,  Copper, 

Zinc,  Silver, 

Hydrogen,  Gold, 

Lead,  Platinum, 

Tin,  —  Graphite  (Carbon). 

Though  Volta  gave  rough  approximations,  the  actual 
numerical  values  of  the  differences  of  potential  in  air  for 
different  pairs  of  metals  were  subsequently  measured  by 
Ayrton  and  Perry,  a  few  of  whose  results  are  tabulated 
here  — 

DIFFERENCE  OF  POTENTIAL  (VOLTS). 


0-210 


Platinum 
Carbon      I0'113 

The  difference  of  potential  between  zinc  and  carbon 
is  the  same  as  that  obtained  by  adding  the  successive  differ- 
ences, or  1-09  volts.1  Volta's  observations  may  therefore 
be  stated  in  the  following  generalized  form,  known  as  Volta's 
Law.  The  difference  of  potential  between  any  two  metals  is 
equal  to  the  sum  of  the  differences  of  potentials  between  the  in- 
tervening metals  in  the  contact-series. 

It  is  most  important  to  notice  that  the  order  of  the  metals 
in  the  contact-series  in  air  is  almost  identical  with  that  of 
the  metals  arranged  according  to  their  electro-chemical 
power,  as  calculated  from  their  chemical  equivalents  and  their 
heat  of  combination  with  oxygen  (see  Table,  Art.  568). 
From  this  it  would  appear  that  the  difference  of  potentials 
between  a  metal  and  the  air  that  surrounds  it  measures  the 
tendency  of  that  metal  to  become  oxidized  by  the  air.  If 
this  is  so,  and  if  (as  is  the  case)  the  air  is  a  bad  conductor 

1  For  the  definition  of  the  volt,  or  unit  of  difference  of  potential,  see 
Art.  381,  p.  342. 


CH.  i.  82,  83]  CONTACT   ACTIONS  79 

while  the  metals  are  good  conductors,  it  ought  to  follow  that 
when  two  different  metals  touch  they  equalize  their  own 
potentials  by  conduction  but  leave  the  films  of  air  that  sur- 
round them  at  different  potentials.  All  the  exact  experi- 
ments yet  made  have  measured  the  difference  of  potentials 
not  between  the  metals  themselves,  but  between  the  air  near 
one  metal  and  that  near  another  metal.  Mr.  John  Brown 
showed  that  while  in  air  iron  is  positive  to  copper,  but  in  an 
atmosphere  of  sulphuretted  hydrogen  iron  is  negative  to 
copper.  He  also  demonstrated  the  existence  on  freshly- 
cleaned  metal  surfaces  of  films  of  liquid  or  condensed  gases ; 
also  that  polished  zinc  and  copper,  when  brought  so  near 
that  their  films  touch,  will  act  as  a  battery. 

82.  Contact  Actions.  —  A  difference  of  potential  is  also 
produced  by  the  contact  of  two  dissimilar  liquids  with  one 
another. 

A  liquid  and  a  metal  in  contact  with  one  another  also 
exhibit  a  difference  of  potential,  and  if  the  metal  tends 
to  dissolve  into  the  liquid  chemically  there  will  be  an  elec- 
tromotive force  acting  from  the  metal  toward  the  liquid. 

The  thermo-electric  difference  of  potential  at  a  junction 
of  two  metals  is  a  true  contact  difference.  It  is  measured 
by  the  amount  of  heat  produced  (see  Peltier-effect,  Art.  472) 
by  passing  a  current  of  electricity  in  the  reverse  direction 
through  the  junction. 

A  hot  metal  placed  in  contact  with  a  cold  piece  of  the 
same  metal  also  produces  a  difference  of  potential,  electrical 
separation  taking  place  across  the  surface  of  contact. 

Lastly,  it  has  been  shown  by  Sir  Joseph  J.  Thomson  that 
the  surf  ace  of  contact  between  two  non-conducting  substances, 
such  as  sealing-wax  and  glass,  is  the  seat  of  a  permanent 
difference  of  potentials. 

83.  Magneto-electricity.  —  Electric  currents  flowing  along 
in  wires  can  be  obtained  mechanically  by  moving  closed  con- 
ducting circuits  in  the  neighbourhood  of  magnets.     This 
source  is  dealt  with  in  Art.  240. 


80  ELECTRICITY   AND   MAGNETISM        [PT.  i.  84 

84.  Summary.  —  We  have  seen  in  the  preceding  para- 
graphs how  almost  all  conceivable  agencies  may  produce 
electrification  in  bodies.  The  most  important  of  these  are 
friction,  heat,  chemical  action,  magnetism,  and  the  contact  of 
dissimilar  substances.  We  noted  that  the  production  of 
electricity  by  friction  depended  largely  upon  the  molecular 
condition  of  the  surfaces.  We  may  here  add  that  the  differ- 
ence of  potentials  produced  by  contact  of  dissimilar  substances 
also  varies  with  the  temperature  and  with  the  nature  of  the 
medium  (air,  vacuum,  etc.)  in  which  the  experiments  are 
made.  Doubtless  this  source  also  depends  upon  the  mo- 
lecular conditions  of  dissimilar  substances  being  different ;  the 
particles  at  the  surfaces  being  of  different  sizes  and  shapes, 
and  vibrating  with  different  velocities.  Moreover,  they  are 
associated  with  the  electrons  in  ways  that  differ  in  different 
elements  and  compounds.  There  are  (see  Art.  11)  good  rea- 
sons for  thinking  that  the  electricity  of  friction  is  really  due 
to  electricity  of  contact,  excited  at  successive  portions  of  the 
surfaces  as  they  are  moved  over  one  another.  Peclet  found 
rolling  contact  and  sliding  contact  to  produce  equal  effects. 
Apparently  those  substances  stand  higher  in  the  list  which 
most  readily  part  with  their  electrons.  See  Art.  632,  p.  638. 


CHAPTER  II 

MAGNETISM 

LESSON  VIII.  —  Magnetic  Attraction  and  Repulsion 

85.  Lodestones  or  Natural  Magnets.  —  The  name  Magnet 
(Magnes  Lapis)  was  given  by  the  ancients  to  certain  hard 
black  stones  found  in  various  parts  of  the  world,  notably 
at  Magnesia  in  Asia  Minor,  which  possessed  the  property  of 
attracting  to  them  small  pieces  of  iron.     This  magic  property, 
as  they  deemed  it,  made  the  magnet-stone  famous ;    but  al- 
though the  Chinese  seem  to  have  known  the  directive  power 
of  the  magnet  since  A.D.  121,  yet  it  was  not  until  the  tenth  or 
eleventh  century  that  it  was  known  in  Europe  that  this  stone 
possessed  the  remarkable  property  of  pointing  north  and 
south  when  floating  on  a  wooden  raft  on  water  or  hung 
up  by  a  thread.     This  property  was  turned  to  advantage 
in  navigation,  and  from  that  time  the  magnet  received  the 
name  of  Lodestone  1   (or  "  leading-stone  ").     The  natural 
magnet  or  lodestone  is  an  ore  of  iron,  known  to  mineralogists 
as  magnetite  and  having  the  chemical  composition  Fe3O4. 
This  ore  is  found  in  quantities  in  Sweden,  Spain,  the  Isle  of 
Elba,  Arkansas,  and  other  parts  of  the  world,  though  not  al- 
ways in  the  magnetic  condition.     It  frequently  occurs  in 
crystals ;   the  usual  form  being  the  regular  octahedron. 

86.  Artificial  Magnets.  —  If  a  piece  of  hard  iron  be  rubbed 
with  a  lodestone,  it  will  be  found  to  have  also  acquired  the 
properties  characteristic  of  the  stone;    it  will  attract  light 
bits  of  iron,  and  if  hung  up  by  a  thread  it  will  point  north 

1  The  common  spelling  loadstone  is  due  to  misapprehension. 
G  81 


82  ELECTRICITY   AND   MAGNETISM        [PT.  i.  87 

and  south.  Figs.  53  and  54  represent  a  natural  lode- 
stone  and  an  artificial  magnet  of  steel,  each  of  which  has 
been  dipped  into  iron-filings ; 
the  filings  are  attracted  and 
adhere  in  tufts  at  the  ends. 
87.  The  earliest  Book  on 

FIG.  53.  —  Piece  of  Lodestone. 

the  Magnet.  —  Beside  a  few 
stray  references  to  the  at- 
tractive power  of  lodestones, 
the  classic  authors  had  little 

..  FIG.  54.  —  Steel  Bar  Magnet. 

to  say  of  the  magnet.  Lu- 
cretius described  how  iron  rings  could  hang  as  in  a  chain 
from  a  magnet ;  and  Pliny,  the  historian,  narrated  a  num- 
ber of  fabulous  stories  about  the"  power  of  the  magnet. 
The  first  real  book  on  the  subject  was  the  Epistle  on  the 
Magnet  of  Peter  Peregrinus,  a  Picard  knight,  written  in 
1269.  He  calls  the  active  parts  of  the  magnet  its  poles, 
and  tells  how  to  distinguish  them  by  exploring  the  surface 
of  the  magnet  with  a  needle  of  iron  or  steel.  He  called 
one  the  north  pole  (that  which  turns  toward  the  north), 
and  the  other  the  south  pole.  He  showed  that  while  two 
north  poles  will  repel  one  another,  and  two  south  poles 
will  repel  one  another,  there  is  attraction  between  a  north 
pole  and  a  south  pole.  He  found  that  if  a  lodestone  be 
cut  or  broken  into  two  parts,  each  part  will  have  a  north  and 
a  south  pole.  He  also  described  a  primitive  mariners'  compass, 
having  a  lodestone  supported  to  turn  on  pivots,  and  placed 
in  a  circular  box,  surrounded  with  a  fixed  circle  divided  into 
360  degrees,  and  furnished  with  sights  for  taking  observations 
at  sea  or  on  land. 

About  the  beginning  of  the  fourteenth  century  some 
unknown  inventor,  probably  a  navigator  in  Southern  Italy, 
improved  the  compass  by  adding  a  movable  "  card  "  on  which 
were  painted  the  eight  chief  winds  or  "  points  "  of  the  com- 
pass, the  card  being  mounted  upon  a  magnetized  needle,  and 
turning  with  it  on  a  pivot. 


CH.  ii.  88-90]        MAGNETIC   ATTRACTIONS 


83 


88.  Writings  of  Dr.   Gilbert.  —  This  was  all,   or  nearly 
all,  that  was  known  of  the  magnet  until  1600,  when  Dr. 
Gilbert  published  a  large  number  of  magnetic  discoveries  in 
his  famous  work  De  Magnete.     Using  small  compass  needles 
to  explore  the  distribution  of  magnetism  in  a  magnet,  he  found 
that  the  portion  of  the  magnet  which  lies  between  its  two 
poles  seems  less  magnetic.     It  scarcely  attracts  iron  filings ; 
and  all  round  the  magnet,  halfway  between  the  poles,  there 
is  no  attraction  at  all.     This  region  Gilbert  called  the  equa- 
tor of  the  magnet,  and  the  imaginary  line  joining  the  poles 
he    termed    the    axis.     Dr. 

Gilbert  also  discovered  that 
the  power  of  a  lodestone  was 
increased  by  arming  its  poles 
with  caps  or  pole-pieces  of 
soft  iron. 

89.  Magnetic     Needle.  — 
To  investigate  magnetic  forces 
a  magnetic  needle  is  employed. 
This  consists  (Fig.  55)  of  a 
light  needle  cut  out  of  steel, 
and  fitted  with  a  little  cap  of 
brass,  glass,  or  agate,  which 
can  be  poised  upon  a  sharp 

point,  so  as  to  turn  with  very  little  friction.  It  is  rendered 
magnetic  by  being  rubbed  upon  a  magnet ;  and  when  thus 
magnetized  it  will  turn  into  the  north-and-south  position, 
or,  as  we  should  say,  will  set  itself  in  the  "  magnetic  merid- 
ian "  (Art.  157),  p.  134.  The  compass  sold  by  opticians 
for  use  on  land  consists  of  such  a  needle  balanced  above 
a  fixed  card  marked  with  the  "  points  of  the  compass  " ; 
in  the  mariners'  compass  the  card  goes  round  with  the 
needle. 

90.  Magnetic  Attractions  and  Repulsions.  —  If  we  take 
a  magnet  (either  natural  or  artificial)  in  our  hand  and  present 
the  two  "  poles  "  of  it  successively  to  the  north-pointing  end 


FIG.  55.  —  A  Magnetic  NeeJle. 


84 


ELECTRICITY   AND   MAGNETISM        [PT.  i.  91 


of  a  magnetic  needle,  we  shall  observe  that  one  pole  of  the 
magnet  attracts  it,  while  the  other  repels  it  (Fig.  56).  Repeat- 
ing the  experiment  on  the  south-pointing  end  of  the  magnetic 
needle,  we  find  that  it  is  repelled  by  one  pole  and  attracted 
by  the  other ;  and  that  the 
same  pole  which  attracts 
the  north-pointing  end  of 
the  needle  repels  the  south- 
pointing  end. 

If  we  try  a  similar  ex- 
periment on  the  magnetic 
needle,  using  for  a  magnet 
a  second  magnetized  needle 

Which  has  previously  been  FlG-  56-  -  Attraction  between  opposite 

*  J  kinds  of  Poles. 

suspended,  and  which  has 

its  north-pointing  end  marked  to  distinguish  it  from  the 
south-pointing  end,  we  shall  discover  that  the  N-point- 
ing  pole  repels  the  N-pointing  pole,  and  that  the  S-point- 
ing  pole  repels  the  S-pointing  pole ;  but  that  a  N-pointing 
pole  attracts  and  is  attracted  by  a  S-pointing  pole. 

91.  Two  Kinds  of  Magnetic  Poles.  —  There  appear  to  be 
two  opposite  kinds  of  magnetism,  or  two  opposite  kinds  of 
magnetic  poles,  which  attract  or  repel  one  another  in  very 
much  the  same  fashion  as  the  two  opposite  kinds  of  electri- 
fication do ;  and  one  of  these  kinds  of  magnetism  appears  to 
have  a  tendency  to  move  toward  the  north  and  the  other  to 
move  toward  the  south.  It  has  been  proposed  to  call  these 
two  kinds  of  magnetism  "  north-seeking  magnetism  "  and 
"  south-seeking  magnetism,"  but  for  our  present  purpose  it 
is  sufficient  to  distinguish  between  the  two  kinds  of  poles. 
In  common  parlance  the  poles  of  a  magnet  are  called  the 
"  North  Pole "  and  "  South  Pole "  respectively,  and  it 
is  usual  for  the  makers  of  magnets  to  mark  the  N-point-. 
ing  pole  with  a  letter  N.  It  is  therefore  sometimes 
called  the  "  marked "  pole,  to  distinguish  it  from  the  S- 
pointing  or  "  unmarked  "  pole.  We  shall,  to  avoid  any 


CH.  ii.  92,  93]     ATTRACTION  AND   REPULSION  85 

doubt,1  call  that  pole  of  a  magnet  which  would,  if  the  magnet 
were  suspended,  tend  to  turn  to  the  north,  the  "  North- 
seeking  "  pole,  and  the  other  the  "  South-seeking  "  pole. 

We  may  therefore  sum  up  our  observations  in  the  con- 
cise statement :  Like  magnetic  poles  repel  one  another ;  unlike 
poles  attract  one  another.  This  we  may  call  the  first  law  of 
magnetism.  As  with  the  electric  attractions  and  repulsions 
of  rubbed  bodies,  so  with  these  magnetic  attractions  and 
repulsions  the  effects  are  due,  as  we  shall  see,  to  stresses  in 
the  intervening  medium. 

92.  The  two  Poles  inseparable.  —  It  is  impossible  to  ob- 
tain a  magnet  with  only  one  pole.     If  we  magnetize  a  piece 
of  steel  wire,  or  watch  spring,  by  rubbing  it  with  one  pole  of 
a  magnet,  we  shall  find  that  still  it  has  two  poles  —  one  N- 
seeking,  the  other  S-seeking.     And  if  we  break  it  into  two 
parts,  each  part  will  still  have  two  poles  of  opposite  kinds. 

93.  Breaking  a  Magnet.  —  If  we  take  a  thin  strip  of  hard 
steel,  magnetized  so  that  one  end  is  a  N  pole  and  the  other  a 
S  pole,  and  break  it  into  two  or  more  pieces,  each  piece  will 
be  found  to  have  a  pole  at  each  end.     Fig.  57  shows  this.     If 
the  broken  parts  be  closely  joined    these    adjacent   poles 
neutralize  one  another  and  disappear,  leaving  only  the  poles 
at  the  ends  as  before.     If  a  magnet  be  ground  to  powder  each 

1  It  is  necessary  to  be  precise  on  this  point,  as  there  is  some  confusion 
in  the  existing  tej«t-books.  The  cause  of  the  confusion  is  this :  —  If  the 
north-pointing  pole  of  a  needle  is  attracted  by  magnetism  residing  near  the 
North  Pole  of  the  earth,  the  law  of  attraction  (that  unlike  poles  attract) 
shows  us  that  these  two  poles  are  really  magnetically  of  opposite  kinds. 
Which  are  we  then  to  call  north  magnetism?  That  which  is  at  the  N.  pole 
of  the  earth?  If  so,  we  must  say  that  the  N-pointing  pole  of  the  needle 
contains  south  magnetism.  And  if  we  call  that  north  magnetism  which 
points  to  the  north,  then  we  must  suppose  the  magnetic  pole  at  the  north 
pole  of  the  earth  to  have  south  magnetism  in  it.  In  either  case  there  is 
then  a  difficulty.  The  Chinese  and  the  French  call  the  N-pointing  pole  of 
the  needle  a  south  pole,  and  the  S-pointing  pole  a  north  pole.  Lord  Kelvin 
called  the  N-pointing  pole  a  "True  South"  pole.  But  common  practice 
goes  the  other  way,  and  calls  the  N-pointing  pole  of  a  magnet  its  "North" 
pole.  For  experimental  purposes  it  is  usual  to  paint  the  two  poles  of  a 
magnet  of  different  colours,  the  N-seeking  pole  being  coloured  red  and  the 
S-seeking  pole  blue. 


86 


ELECTRICITY  AND   MAGNETISM   [PT.  i.  94,  95 


Fio.  57.  —  Experiment  on  breaking  a  Magnet. 


fragment  will  still  act  as  a  little  magnet  and  exhibit  polarity. 
A  magnet  may  therefore  be  regarded  as  composed  of  many 

little  magnets  put 
together,  so  that 
their  like  poles  all 
face  one  way. 
Such  an  arrange- 
ment is  indicated  in  Fig.  58,  from  which  it  will  be  seen 
that  if  the  magnet  be  broken  asunder  across  any  part,  one 
face  of  the  fracture  will  present  only  N  poles,  the  other  only 
S  poles.  This  would 
be  true  no  matter  how 
small  the  individual 


N 


S'N' 


n 
n        .s- 

n       x 

%  s 

n  —  1 

It          S 

\]}       s 

n       .s 
"      s 

n      s 
n      s 

n       ,s 
n       s 

N  SN  S 

FIG.  58.  —  Bar  Magnet  built  up  of  small  Bars. 


particles. 

94.  The    Earth   a 
Magnet.  —  The  great- 
est of  Gilbert's  discoveries  was  that  of  the  inherent  magnetism 
of  the  earth.     The  earth  is  itself  a  great  magnet,  whose  "  poles  " 
coincide  nearly,  but  not  quite,  with  the  geographical  north 
and  south  poles,  and  therefore  it  causes  a  freely-suspended 
magnet  to  turn    into    a    north-and-south    position.      Gil- 
bert had  some  lodestones  cut  to  the  shape  of  spheres  to 
serve  as  models  of  the  globe  of  the  earth.     Such  a  globular 
magnet  he  called  a  terrella.     He  found  that  small  magnets 
turned  toward  the  poles  of  the  terrella,  and  dip,  as  compass- 
needles  do,  toward  the  earth. 

The  subject  of  Terrestrial  Magnetism  is  treated  of  in  Les- 
son XII.  It  is  evident  from  the  first  law  of  magnetism 
that  the  magnetic  condition  of  the  northern  regions  of  the 
earth  must  be  the  opposite  to  that  of  the  north-seeking  pole 
of  a  magnetized  needle.  Hence  arises  the  difficulty  of  lan- 
guage alluded  to  on  page  85. 

95.  Magnetic  Force.  —  The  force  with  which  a  magnet 
attracts  or  repels  another  magnet,  or  any  piece  of  iron  or 
steel,  we  shall  call  magnetic  force.1     The  force  exerted  by  a 

1  See  footnote  on  "Force,"  Art.  177,  p.  151. 


CH.  ii.  96,  97]         MAGNETIC   SUBSTANCES  87 

magnet  upon  a  bit  of  iron  or  on  another  magnet  is  not  the 
same  at  all  distances,  the  force  being  greater  when  the  magnet 
is  nearer,  and  less  when  the  magnet  is  farther  off.  (See  Art. 
131,  p.  109,  on  law  of  magnetic  force.) 

Whenever  a  force  acts  thus  between  two  bodies,  it  acts 
on  both  of  them,  tending  to  move  both.  A  magnet  will 
attract  a  piece  of  iron,  and  a  piece  of  iron  will  attract  a  mag- 
net. 

Fix  a  magnet  upon  a  piece  of  cork  and  float  it  in  a  basin 
of  water  (Fig.  59) ;  it  will  move  across  the  basin  when  a  piece 
of  iron  is  held  near.  A  compass  needle  thus  floated  turns 
round  and  points  north  and  south  ;  but  it  does  not  rush  to- 
wards the  north  as  a  whole,  nor  towards  the  south.  The 
reason  of  this  will  be  explained  later,  in  Art.  131,  p.  109. 

Gilbert  suggested  that  the  force  of  a  magnet  might  be 
measured  by  making  it  attract  a  piece  of  iron  hung  to  one 
arm  of  a  balance,  weights  being  placed  in  the  scale-pan 
hanging  to  the  other  arm ;  and  he  found,  by  hanging  the 
magnet  to  the  balance  and  placing  the 
iron  beneath  it,  that  the  effect  produced 
was  the  same.  The  action  and  reaction 
are  then  equal  for  magnetic  forces. 

96.  Magnetic    Substances.  —  A    dis- 
tinction was  drawn  by  Gilbert  between 

magnets    and    magnetic    substances.     A     <IQ'  59'Magiet!mg  Bar 
magnet  attracts  only  at  its  poles,  and 
they  possess  opposite  properties.     But  any  part  of  a  lump 
of  soft  iron  will  attract  either  pole  of  the  magnet.     It  has  no 
distinguishable  fixed  "  poles,"  and  no  magnetic  "  equator." 
A  true  magnet  has  poles,  one  of  which  is  repelled  by  the  simi- 
lar pole  of  another  magnet. 

97.  Other  Magnetic  Materials.  —  In  addition  to  iron  (and 
steel)  the  metals  nickel  and  cobalt  are  recognized  as  magnetic 
as  they  are  attracted  by  a  magnet.     It  has  also  been  supposed 
that  chromium  and  manganese  are  slightly  magnetic,  but 
practically  they  are  non-magnetizable  (Art.  396,  p.  361). 


88  ELECTRICITY   AND   MAGNETISM   [PT.  i.  98,  99 

Only  nickel  and  cobalt  are  at  all  comparable  with  iron  and 
steel  in  magnetic  power,  and  even  they  are  far  inferior.  Some 
of  the  alloy  steels  (see  Art.  396)  are  magnetic,  for  example, 
nickel  steel,  chrome  steel,  and  tungsten  steel.  Manganese 
steel  is  non-magnetic  :  yet  the  alloy  of  manganese  with  alumin- 
ium and  copper,  and  the  alloy  of  manganese  with  bismuth, 
are  both  highly  magnetic.  Other  bodies,  sundry  salts  of 
iron  and  other  metals,  paper,  porcelain,  and  oxygen  gas  are 
also  very  feebly  attracted  by  a  powerful  magnet.  Liquid 
oxygen  is  attracted  to  the  poles  of  magnets. 

98.  Diamagnetism.  —  A  number  of  bodies,  notably  bis- 
muth, antimony,  phosphorus,  and  copper,  are  apparently 
repelled  from  the  poles  of  a  magnet.     Such  bodies  are  called 
diamagnetic  bodies ;  a  fuller  account  of  them  will  be  found  in 
Arts.  398  to  402,  p.  362. 

99.  Induction  of  Magnetism.  —  Magnetism  may  be  com- 
municated to  a  piece  of  iron  without  actual  contact  with  a 
magnet.     If  a  short,  thin  unmagnetized  bar  of  iron  be  placed 

near  some  iron  filings,  and  a  mag- 
net be  brought  near  to  the  bar, 
the  presence  of  the  magnet  will 
FIG.  GO.  —  Magnetization  by  in-     induce  magnetism  in  the  iron  bar. 

fluence  of  a  Bar  Magnet. 

and  it  will  now  attract  the  iron 

filings  (Fig.  60) .  This  inductive  action  is  very  similar  to  that 
observed  in  Lesson  III.  to  take  place  when  a  non-electrified 
body  was  brought  under  the  influence  of  an  electrified  one. 
The  analogy,  indeed,  goes  further  than  this,  for  it  is  found  that 
the  iron  bar  thus  magnetized  by  induction  will  have  two  poles ; 
the  pole  nearest  to  the  pole  of  the  inducing  magnet  being  of 
the  opposite  kind,  while  the  pole  at  the  farther  end  of  the  bar 
is  of  the  same  kind  as  the  inducing  pole.  Those  bodies  in 
which  a  magnetizing  force  produces  a  high  degree  of  magnet- 
ization are  said  to  possess  a  high  permeability.  It  will  be 
shown  presently  that  magnetic  influence  takes  place  along 
certain  directions  called  lines  of  magnetic  force,  which  may 
pass  either  through  iron  and  other  magnetic  media,  or  through 


CH.  ii.  100]       ATTRACTION   ACROSS   BODIES 


89 


air,  vacuum,  glass,  or  other  non-magnetic  media :  and,  since 
induction  goes  on  most  freely  in  bodies  of  high  magnetic 
permeability,  the  magnetic  lines  are  sometimes  (though  not 
too  accurately)  said  to  "  pass  by  preference  through  magnetic 
matter,"  or,  that  "  magnetic  matter  conducts  the  lines  of 
force." 

100.  Attraction  across  Bodies.  —  If  a  sheet  of  glass,  or 
wood,  or  paper,  be  interposed  between  a  magnet  and  the 
piece  of  iron  or  steel  it  is  attracting,  it  will  still  attract  it  as  if 
nothing  were  interposed.  A  magnet  sealed  up  in  a  glass 
tube  still  acts  as  a  magnet.  Lucretius  found  a  magnet  put 
into  a  brass  vase  attracted  iron  filings  through  the  brass. 
Gilbert  surrounded  a  magnet  by  a  ring  of  flames,  and  found 
it  still  to  be  subject  to  magnetic  attraction  from  without. 
Across  water,  vacuum,  and  all  known  substances,  the  mag- 
netic forces  will  act ; 
with  the  single  appar- 
ent exception,  how- 
ever, that  magnetic 
force  will  not  act 
across  a  screen  of  iron 
or  other  magnetic  ma- 
terial, if  sufficiently 
thick.  If  a  small 
magnet  is  suspended  inside  a  hollow  ball  made  of  iron,  no 
outside  magnet  will  affect  it.  The  reason  being  that  the 
magnetic  lines  of  force  are  conducted  off  laterally  through  the 
iron  instead  of  penetrating  through  it.  A  hollow  shell  of  iron 
therefore  acts  as  a  magnetic  screen,  and  shields  the  space  in- 
side it  from  magnetic  influences. 

Fig.  61  illustrates  the  way  in  which  a  cylinder  of  soft  iron 
screens  the  space  interior  to  it  from  the  influence  of  an  exter- 
nal magnet.  A  compass  needle  placed  at  P  inside  the  cylin- 
der is  not  affected  by  the  presence  of  the  magnet  outside,  for 
its  lines  of  magnetic  force  are  drawn  off  laterally.  Similarly 
a  magnet  inside  is  screened  from  affecting  outside  space. 


FIG.  61.  —  Magnetic  Screening. 


90  ELECTRICITY  AND   MAGNETISM      [FT.  i.  101 

Although  magnetic  induction  takes  place  at  a  distance 
across  an  intervening  layer  of  air,  glass,  or  vacuum,  there  is 
no  doubt  that  the  intervening  medium  is  directly  concerned 
in  the  transmission  of  the  magnetic  force,  though  the  true 
medium  is  probably  the  "  ether  "  of  space  surrounding  the^ 
molecules  of  matter,  not  the  molecules  themselves. 

We  now  can  see  why  a  magnet  should  attract  a  not-pre- 
viously-magnetized piece  of  iron ;  it  first  magnetizes  it  by 
induction  and  then  attracts  it :  for  the  nearest  end  will  have 
the  opposite  kind  of  magnetism  induced  in  it,  and  will  be 
attracted  with  a  force  exceeding  that  with  which  the  more 
distant  end  is  repelled.  But  induction  precedes  attraction. 

101.  Retention  of  Magnetization.  —  Not  all  magnetic 
substances  can  become  magnets  permanently.  Lodestone, 
hard  steel,  and  nickel  retain  permanently  the  greater  part  of 
the  magnetism  imparted  to  them.  Pieces  of  really  soft 
iron  and  of  soft  mild  steel,  though  they  can  be  temporarily 
highly  magnetized,  lose  their  magnetism 
directly  the  magnetizing  force  is  re- 
moved. Cast  iron  and  many  impure 
qualities  of  wrought  iron  also  retain 
magnetism  imperfectly.  The  softer 
and  purer  a  specimen  of  iron  is,  the 
more  lightly  is  its  residual  magnetism 
retained.  The  following  experiment 
FIG.  62.  — Magnetic"  with  a  bar  magnet  illustrates  the  mat- 
Chain.  ^er  .  —  LG£  a  few  pieces  of  soft  iron  rod, 
or  a  few  soft  iron  nails  be  taken.  If  one  of  these  (see  Fig.  62) 
be  placed  in  contact  with  the  pole  of  a  permanent  steel  mag- 
net, it  is  attracted  to  it,  and  becomes  itself  a  temporary 
magnet.  Another  bit  of  iron  may  then  be  hung  to  it,  and 
another,  until  a  chain  of  four  or  five  pieces  is  built  up.  But 
if  the  steel  magnet  be  removed  from  the  top  of  the  chain,  all 
the  rest  drop  off,  and  are  found  to  be  no  longer  magnetic.  A 
similar  chain  of  steel  needles  may  be  formed,  but  they  will 
retain  permanently  most  of  their  magnetism. 


CH.  ii.  102]  THEORIES   OF   MAGNETISM  91 

It  will  be  found,  however,  that  a  hard  steel  rod  is  more 
difficult  to  magnetize  than  an  iron  rod  of  the  same  dimensions. 
It  is  harder  to  get  the  magnetism  into  hard  steel  than  into 
soft  iron,  and  it  is  harder  to  get  the  magnetism  out  of  steel 
than  out  of  iron ;  for  the  hard  steel  retains  the  magnetism 
once  put  into  it.  This  power  of  resisting  magnetization,  or 
demagnetization,  is  called  retentivity,  and  it  is  measured  by 
the  coercive  force  (see  Art.  394).  The  retentivity  of  hardened 
steel  is  great ;  that  of  soft  steel  or  wrought  iron  is  very  small. 
The  harder  the  steel,  the  greater  its  retentivity.  Form 
affects  retentivity.  Elongated  forms  and  those  shaped  as 
closed  or  nearly  closed  circuits  retain  their  magnetism  better 
than  short  rods,  balls,  or  cubes. 

102.  Theories  of  Magnetism.  —  The  student  will  not  have 
failed  to  observe  the  analogies  between  the  phenomena  of  at- 
traction, repulsion,  induction,  etc.,  of  magnetism  and  those 
of  electricity.  Yet  the  two  sets  of  phenomena  are  quite 
distinct.  A  positively  electrified  body  does  not  attract 
either  the  North-pointing  or  the  South-pointing  pole  of  the 
magnet  as  such ;  in  fact,  it  attracts  either  pole  quite  irrespec- 
tive of  its  magnetism,  just  as  it  will  attract  any  other  body. 
There  does  exist,  indeed,  a  direct  relation  between  magnets 
and  currents  of  electricity,  as  will  be  later  explained.  There 
is  none  known,  however,  between  magnets  and  stationary 
charges  of  electricity. 

Formerly  it  was  the  fashion  to  speak  of  a  magnetic  fluid 
or  fluids ;  it  is,  however,  absolutely  certain  that  magnetism  is 
not  a  fluid,  whatever  else  it  may  be.  The  term  is  a  relic  of 
bygone  times.  A  magnet  when  rubbed  upon  a  piece  of  steel 
magnetizes  it  without  giving  up  or  losing  any  of  its  own  magnet- 
ism. A  fluid  cannot  possibly  propagate  itself  indefinitely 
without  loss.  The  arguments  to  be  derived  from  the  behav- 
iour of  a  magnet  on  breaking,  and  from  other  experiments 
narrated  in  Lesson  X.,  are  even  stronger.  No  theory  of  mag- 
netism will  be  propounded  until  these  facts  have  been  placed 
before  the  student. 


92 


ELECTRICITY   AND   MAGNETISM     [PT.  i.  103,  104 


103.  Forms  of  Magnets.  —  Natural  magnets  are  usually 
of  irregular  form,  though  they  are  sometimes  reduced  to  regu- 
lar shapes,  such  as  rods  or  spheres,  by  cutting  or  grinding. 
Formerly  it  was  the  fashion  to  mount  rectangular  blocks  of 
lodestone  with  soft  iron  cheeks  or  "  armatures  "  to  serve  as 
pole-pieces. 

For  scientific  experiments  bar  magnets  of  hardened  steel 
are  commonly  used ;  but  for  many  purposes  the  horse-shoe 
shape  is  preferred.  In  the  horse-shoe  magnet  the  poles  are 
bent  round  so  as  to  approach  one  another,  the  advantage  here 
being  that  so  both  poles  can  attract  one  piece  of  iron.  The 


FIG.  63.  —  Horse-shoe  Magnets :   Three  Forms. 

"  armature,"  or  "  keeper,"  as  the  piece  of  soft  iron  placed 
across  the  poles  is  named,  is  itself  rendered  a  magnet  by  in- 
duction ;  hence,  when  both  poles  magnetize  it,  the  force  with 
which  it  is  attracted  to  the  magnet  is  the  greater.  A  horse- 
shoe magnet  will  lift  three  or  four  times  as  heavy  a  piece  of 
iron  as  that  which  can  be  lifted  by  a  bar  magnet  of  equal 
weight.  Fig.  63  shows  three  forms  of  horse-shoe  magnet. 
Fig.  63  a  is  the  ordinary  Sheffield  pattern.  Fig.  63  c,  which  is 
of  a  form  more  nearly  constituting  a  closed  circuit,  is  more 
constant  in  its  power. 

104.    Laminated  Magnets.  —  Long  thin  steel  magnets  are 
more  powerful  in  proportion  to  their  weight  than  thicker 


CH.  ii.  105]     METHODS   OF   MAGNETIZATION 


93 


FIG.  64.  FIG.  65. 

Laminated  Magnets. 


ones.  Hence  it  was  proposed  by  Scoresby  1  to  construct 
compound  magnets,  consisting  of  thin  laminae  of  steel  sepa- 
rately magnetized,  and 
afterwards  bound  to- 
gether in  bundles  (Fig. 
64).  These  laminated 
magnets  have  little  ad- 
vantage over  simple  bars 
of  steel.  Compound  horse-shoe  magnets  are  sometimes 
used :  the  plates,  separately  magnetized,  are  assembled  as 
in  Fig.  65. 

LESSON  IX.     Methods  of  Making  Magnets 

105.    Magnetization  by  Touch.  —  It  has  been  so  far  as- 
sumed that  bars  or  needles  of  steel  were*  to  be  magnetized 

by  simply  touching  them, 
or  stroking  them  from  end 
to  end  with  the  pole  of 
a  permanent  magnet  of 
lodestone  or  steel.  A 
more  certain  effect  is  pro- 
duced if  the  needle  or  strip 
of  steel  is  drawn  from  its 
middle  to  its  end,  as  in  Fig. 
66,  over  the  pole  of  a  power- 
ful magnet ;  one  half  of 
the  needle  being  drawn 
across  one  of  the  poles, 
and  then  the  other  half 
across  the  other  pole.  The 
last  touched  point  of  the 
needle  will  be  a  pole  of  op- 
posite kind  to  that  used  to  touch  it.  There  are,  however, 
better  ways  of  magnetizing  a  bar. 

1  A  similar  suggestion  was  made  by  Geuns  of  Venlo  in  1768,  using  horse- 
shoe magnets.     Similar  magnets  were  constructed  later  by  Jamin. 


FIG.  66.  —  Magnetization  by  Touch. 


94          ELECTRICITY   AND   MAGNETISM       [PT.  i.  106-108 

106.  Magnetization  by  Divided  Touch.  —  In  this  method 
the  bar  to  be  magnetized  is  laid  down  horizontally ;  two  bar 

magnets  are  then  placed  down 
upon  it,  their  opposite  poles 
being  together.  They  are 
then  drawn  asunder  from  the 
middle  of  the  bar  towards  its 
FIG.  67. -Method  of  Divided  Touch.  ends  several  times,  stroking 

always    towards    the    ends. 

The  bar  is  then  turned  over,  and  the  operation  repeated, 
taking  care  to  leave  off  at  ends  (see  Fig.  67).  The  process 
is  more  effectual  if  the  ends  of  the  bar  are  meantime  supported 
on  the  poles  of  other  bar  magnets,  the  poles  being  of  the  same 
names  as  those  of  the  two  magnets  above  them  used  for 
stroking  the  steel  bar. 

107.  Magnetization  by  Double  Touch.  —  Another  method, 
known  as  double  touch,  differs  slightly  from  that  last  described. 
A  piece  of  wood  or  cork  is  interposed  between  the  ends  of  the 
two  bar  magnets  employed,  and  they  are  then  both  moved 
backwards  and  forwards  along  the  bar  that  is  to  be  magne- 
tized.    By  none  of  these  methods,  however,  can  a  steel  bar 
be  magnetized  beyond  a  certain  degree  of  intensity. 

108.  Magnetization  derived  from  the  Earth.  —  The  mag- 
netism of  the  earth  may  be  utilized  where  no  other  permanent 
magnet  is  available  to  magnetize  a  bar  of  steel.     Gilbert 
found  that  iron  bars  set  upright  for  a  long  time  acquire 
magnetism  from  the  earth.     If  a  steel  poker  be  held  in  the 
magnetic  meridian,  with  the  north  end  dipping  down,  and  in 
this  position  be  struck  with  a  wooden  mallet,  it  will  be  found 
to   have   acquired   magnetic   properties.     All  vertical   iron 
columns  in  our  northern  latitudes  are  found  to  have  their 
lower  ends  N-poles  and  their  upper  ends  S-poles.     In  Aus- 
tralia and  the  southern  hemisphere  the  tops  of  iron  columns 
are  N-poles.     Wires  of  steel  subjected  to  torsion  while  in 
the  magnetic  meridian  are  also  found  to  be  thereby  mag- 
netized. 


JH.  ii.  109-111]     HEAT    TREATMENT    OF    STEEL  95 

109.  Magnetization  after  Heating.  —  Gilbert  discovered 
also  that  if    a  bar  of  steel  be  heated  to  redness,  and  cooled, 
either  slowly  or  suddenly,  while  lying  in  the  magnetic  merid- 
ian, it  acquires  magnetic  polarity.     No  such   property  is 
acquired  if  it  is  cooled  while  lying  east  and  west.     It  has  been 
proposed  to  make  magnets  by  placing  hot  bars  of  steel  to 
cool  between  the  poles  of  very   powerful   electromagnets ; 
or  to  cast  magnets  of  iron  in  moulds  lying  in  an  intense 
magnetic  field.     These  plans  are  not  recommended. 

110.  Magnetization  by  Currents  of  Electricity.  —  A  cur- 
rent of  electricity  circulating  in  a  spiral  wire  wound  around 
a  core  of  iron  or  steel  magnetizes  it  more 

powerfully  than  any  of  the  preceding  methods. 
In  the  case  of  a  soft  iron  core,  it  is  only  a 
magnet  while  the  current  continues  to  flow. 
Such  a  combination  is  termed  an  Electro- 
magnet ;  it  is  fully  described  in  Lesson  XXXI. 
Fig.  68  depicts  a  common  form  of  electro-  FIG.  68.  —  Electro- 
magnet having  two  coils  of  insulated  copper 
wire  wound  upon  bobbins  that  are  placed  upon  the  limbs  of  a 
soft  iron  core.  The  armature  is  also  of  soft  iron  of  sufficient 
thickness.  Steel  bars  may  be  magnetized  by  drawing  them 
over  the  poles  of  such  an  electromagnet  while  the  latter  is 
excited  by  the  circulation  of  the  electric  current.  Steel 
horse-shoes  are  best  magnetized  by  placing  their  poles  in  con- 
tact with  the  poles  of  a  very  powerful  electromagnet,  the 
current  of  which  is  then  switched  on. 

111.  Hardening  and  Tempering  of  Steel  for  Magnets.  — • 
There  are  two  ways  of  hardening  steel:    (1)  by  suddenly 
cooling  it  from  a  bright  red  temperature ;    (2)  by  compress- 
ing it  under  hydraulic  pressure  while  it  cools  slowly.     If  rods 
of  steel  are  heated  brilliantly  red,  and  then  quenched  in 
water,  oil,  or  mercury,  they  become  intensely  brittle  and 
glass-hard.     To  temper  hard  steel  it  is  then  gently  reheated 
to  near  a  very  dull  red  heat,  when  in  a  few  moments  it  softens 
slightly  while  acquiring  a  straw  tint.     If  let  down  still  further 


96          ELECTRICITY   AND   MAGNETISM       [PT.  i.  112,  113 

by  continuing  the  reheating  it  becomes  a  blue  tint,  and  is 
springy  and  flexible.  Short  bar  magnets  retain  most  mag- 
netism if  left  glass-hard  without  tempering.  But  steel  mag- 
nets whose  length  is  more  than  twenty  times  their  thickness 
retain  their  magnetism  better  if  tempered  down  to  a  straw 
or  even  to  a  blue  tint. 

112.  Destruction  of  Magnetism.  —  A  steel  magnet  loses 
its  magnetism  partially  or  wholly  if  subjected  to  rough  usage, 
or  if  purposely  hit  or  knocked  about.     Newly  magnetized 
magnets  lose  more  strength  by  rough  treatment  than  those 
which  have  been  long  magnetized.     A  magnet  loses  it  mag- 
netism, as  Gilbert  showed,  on  being  raised  to  a  bright  red- 
heat.     The  slightest  vibration  will  destroy  any  magnetism 
remaining  in  annealed  soft  iron. 

113.  Magnets   of   Unvarying   Strength.  —  Ordinary    steel 
magnets  have  by  no  means  a  permanent  or  constant  mag- 
netism.    They  soon  lose  a  considerable  percentage  of  their 
magnetism,  and  the  decay  continues  slowly  for  months  and 
years.     Every  shock  or  jolt  to  which  they  are  subjected, 
every  contact  with  iron,  every  change  of  temperature  weakens 
them.     Every  time  that  the  keeper  is  slammed  on  to  a  horse- 
shoe magnet  it  is  weakened ;   but  sudden  detachment  of  the 
keeper  strengthens  the  magnet.     For  the  purpose  of  making 
magnetic  measurements,  and  for  use  as  controlling  magnets 
of  galvanometers,  magnets  are,  however,  required  that  shall 
possess  the  utmost  constancy  in  their  strength.     Magnets 
of  unvarying  strength  may  be  made  by  attention  to  the  fol- 
lowing points.     Select  a  good  tungsten  steel  or  molybdenum 
steel.     Choose  a  form  either  of  a  nearly  closed  circuit  or  of 
a  very  long  rod.     Let  the  steel  be  hardened  as  much  as 
possible    (see   Art.   Ill   above),   then   boiled   or   placed   in 
steam  at  100°  for  twenty  or  thirty  hours  or  more.     Then 
magnetize   as   fully   as  possible,  and   then   heat   again  for 
five  hours  in  steam.     Magnets  of  a  shape  constituting  a 
nearly  closed  circuit  are  more  constant  than  short  straight 
magnets. 


CH.  ii.  114,  115]      MAGNETIC    SATURATION  97 

114.  Effects  of  Heat  on  Magnetization.  —  If  a  permanent 
steel  magnet  be  warmed  by  placing  it  in  hot  or  boiling  water, 
its  strength  will  be  thereby  lessened,   though  it  recovers 
partially    on    cooling.     Chilling    a    magnet    increases    tem- 
porarily its  strength.     Iron  and  steel  cease  to  be  attracted 
by  a  magnet  at  a  bright  red  heat.     Pure  iron  is  transformed 
at  760°  C.  to  an  almost  non-magnetic  state;    the  transfor- 
mation-point of  nickel  is  320°  C.,  that  of  cobalt   1120°  C. 
On  cooling  down  to  the  transformation  point  the  metal  re- 
gains its  magnetizability.     It  has  been  surmised  that  other 
metals  would  become  magnetic  if  cooled  to  a  low  enough 
temperature.     Dewar  observed  that  the  magnetic  suscep- 
tibility of  iron,  when  cooled  to  near  —  180°  C.  in    liquid 
oxygen,  is  nearly  twice  as  high  as  at  0°  C. 

If  steel  at  a  bright  red  heat  be  cooled  slowly,  a  point  is 
reached  at  which  there  is  a  sudden  molecular  change  accom- 
panied by  a  rapid  evolution  of  heat  sufficient  to  arrest  the 
darkening  tint  and  causing  the  metal  to  glow  red  again. 
This  phenomenon  is  called  recalescence ;  it  marks  the  tran- 
sition to  the  magnetizable  state.  Steel  quenched  in  cold 
water  above  the  temperature  of  recalescence  is  very  hard, 
and  capable  of  great  magnetic  retentivity.  The  magnetic 
metals  at  high  temperatures  do  not  become  diamagnetic, 
but  are  still  feebly  magnetic,  their  susceptibility  at  tem- 
peratures above  the  transformation-point  varying  inversely 
as  the  absolute  temperature. 

115.  Magnetic    Saturation.  —  A    magnet    to    which    as 
powerful  a  degree  of  magnetization  as  it  can  attain  to  has 
been  given  is  said  to  be  relatively  saturated.     A  recently 
magnetized  magnet  will  occasionally  appear  to  acquire  a 
higher  degree  of  magnetism  than  it  is  able  to  retain  per- 
manently.    Thus    a    horse-shoe-shaped    steel    magnet    will 
support   a   greater   weight   immediately   after   being   mag- 
netized than  it  will  do  after  its  armature  has  been  once  re- 
moved from  its  poles.     Even  soft  iron  after  being  mag- 
netized retains  a  small  amount  of  magnetism  when  its  tern- 


98  ELECTRICITY   AND   MAGNETISM    [PT.  i.  116,  117 

porary  magnetism  has  disappeared.     This  small  remaining 
magnetic  charge  is  spoken  of  as  residual  magnetism. 

116.  Strength  of  a  Magnet.  —  The  "  strength  "  of  a  mag- 
net does  not  mean  the  same  thing  as  its  "  lifting  power." 
Its  lifting  power  is  a  very  uncertain  quantity,  depending 
not  only  on  the  shape  of  its  polar  surfaces,  but  on  the  shape 
and  quality  of  the  mass  of  iron  used  as  load.     Consequently 
the  "  strength  "  of  a  magnet  pole  must  be  measured  by  the 
magnetic  force  which  it  exerts  at  a  distance  on  other  mag- 
nets.    Thus,   suppose  there  are   two   magnets,   A  and  B, 
whose  strengths  we  compare  by  making  them  each  act  upon 
the  N-pole  of  a  third  magnet  C.     If  the  N-pole  of  A  repels 
C  with  twice  as  much  force  as  that  with  which  the  N-pole 
of  B  placed  at  the  same  distance  would  repel  C,  then   we 
should  say  that  the  "  strength  "  of  A  was  twice  that  of  B. 
Another   way   of   putting   the   matter  is   to   say  that  the 
"  strength  "  of  a  pole  is  the  amount  of  free  magnetism  at 
that  pole.     By  adopting  the  unit  of  strength  of  magnet  poles 
as  denned  in  Art.  142,  we  can  express  the  strength  of  any 
pole  in  numbers  as  so  many  "  units  "  of  strength. 

117.  Lifting   Power.  —  The   lifting   power   of   a   magnet 
(also  called  its  portative  force)  depends  both  upon  the  form 
of  the  magnet  and  on  its  magnetic  strength.     A  horse-shoe 
magnet  will  lift  a  load  three  or  four  times  as  great  as  a  bar 
magnet  of  the  same  weight  will  lift.     A  long  bar  magnet 
will  lift  more  than  a  short  bar  magnet  of  equal  strength.     A 
bar  magnet  with  a  rounded  or  chamfered  end  will  lift  more 
than  a  similar  bar  with  a  flat  or  expanded  end,  even  though 
both  are  equally  magnetized.     Also  the  lifting  power  of  a 
magnet  grows  in  a  very  curious  and  unexplained  way  by 
gradually  increasing  the  load  on  its  armature  day  by  day 
until  it  bears  a  load  which  at  the  outset  it  could  not  have 
done.     Nevertheless,  if  the  load  is  so  increased  that  the  arma- 
ture is  torn  off,  the  power  of  the  magnet  falls  at  once  to  its 
original  value.     The  attraction  between  a  powerful  electro- 
magnet and  its  armature  may  amount  to  230  Ibs.  per  square 


CH.  ii.  118]  MAGNETIC   FIELD  99 

inch,  or  16,000  grammes  per  square  centimetre  of  contact 
surface  (see  Art.  415) ;  while  that  of  a  permanent  steel  mag- 
net seldom  reaches  a  quarter  of  that  amount.  Small  mag- 
nets lift  a  greater  load  in  proportion  to  their  own  weight 
than  large  ones,1  because  the  lifting  power  is  proportional 
to  the  polar  surface,  other  things  being  equal.  A  good  steel 
horse-shoe  magnet  weighing  itself  1  Ib.  ought  to  lift  25  Ibs. 
weight.  Sir  Isaac  Newton  is  said  to  have  possessed  a  little 
lodestone  mounted  in  a  signet  ring  which  would  lift  a  piece 
of  iron  200  times  its  own  weight. 

LESSON  X.  —  Distribution  of  Magnetism 

118.  Magnetic  Field.  —  The  space  all  round  a  magnet  per- 
vaded by  the  magnetic  forces  is  termed  the  "field"  of  that 
magnet.  It  is  most  intense  near  the  poles  of  the  magnet, 
and  is  weaker  and  weaker  at  greater  distances  away.  At 
every  point  in  a  magnetic  field  the  force  has  a  particular 
strength,  and  acts  in  a  particular  direction.  It  is  possible 
at  any  point  in  a  magnetic  field  to  draw  a  line  in  the  direc- 
tion of  the  resultant  magnetic  force  acting  at  that  point. 
The  whole  field  may  in  this  way  be  mapped  out  with  mag- 
netic lines  (Art.  121).  For  a  horse-shoe  magnet  the  field 
is  most  intense  between  the  two  poles,  and  the  lines  of  mag- 
netic force  are  curves  which  pass  from  one  pole  to  the  other 
across  the  field.  A  practical  way  of  investigating  the  dis- 
tribution of  the  magnetic  lines  in  a  field  is  given  in  Art.  121, 
under  the  title  "  Magnetic  Figures."  When  the  armature 
is  placed  upon  the  poles  of  a  horse-shoe  magnet,  the  force  of 

1  James  Hamilton,  in  1729,  discovered  that  the  lifting  power  of  a  magnet 
is  proportional  to  the  square  of  the  cube-root  of  its  weight ;  and  Bernoulli 
gave  the  following  rule  for  finding  the  lifting  power  p  of  a  magnet  whose 
weight  was  w  :  — 

p  =  a-\/w2, 

where  a  is  a  constant  depending  on  the  goodness  of  the  steel  and  the  method 
of  magnetizing  it.  In  the  best  steel  horse-shoe  magnets  made  at  Haarlem 
by  Van  Wetteren  this  coefficient  was  from  19.5  to  23,  the  weights  being 
expressed  in  kilogrammes. 


100  ELECTRICITY   AND   MAGNETISM    [PT.  i.  119,  120 

the  magnet  on  all  the  external  regions  is  weakened,  for  the 
induction  now  goes  on  through  the  iron  of  the  keeper,  not 
through  the  surrounding  space.  In  fact  a  closed  system  of 
magnets  —  such  as  that  made  by  placing  four  bar  magnets 
along  the  sides  of  a  square,  the  N-pole  of  one  touching  the  S- 
pole  of  the  next  —  has  no  external  field  of  force.  A  ring  of 
steel  may  thus  be  magnetized  so  as  to  have  neither  external 
field  nor  poles ;  or  rather  any  point  in  it  may  be  regarded 
as  a  N-pole  and  a  S-pole,  so  close  together  that  they  neu- 
tralize one  another's  forces. 

119.  Normal  Distribution.  —  In  an  ordinary  bar  magnet 
the  poles  are  not  quite  at  the  ends  of  the  bar,  but  a  little 
way  from  it ;  and  it  can  be  shown  that  this  is  a  result  of  the 
way  in  which  the  surface  magnetism  is  distributed  in  the  bar. 
A  very  long,  thin,  uniformly  magnetized  bar  has  its  poles 
at  the  ends ;    but  in  ordinary  thick  magnets  the  "  pole  " 
occupies  a  considerable  region,  the  "  free  magnetism  "  fall- 
ing off  gradually  from  the  ends  of  the  bar.     In  each  region, 
however,  a  point  can  be  generally  determined  at  which  the 
resultant  magnetic  forces  act,  and  which  may  for  most  pur- 
poses be  considered  as  the   "  pole."     In  certain  cases  of 
irregular  magnetization  it  is  possible  to  have  one  or  more 
poles  between  those  at  the  ends.     Such  poles  are  called  con- 
sequent poles  (see  Fig.  72).     Sometimes  the  two  poles  of  a 
magnet  do  not  seem  to  be  equally  strong.     This  is  due  to 
irregularities  in  the  shape  of  the  magnet  or  to  inequalities 
in  the  hardening  or  magnetizing  of  the  steel.     Actually  the 
total  quantity  of  magnetism  in  one  half  is  always  exactly 
equal  to  that  in  the  other  half. 

120.  Lamellar     Distribution     of     Magnetism.      Magnetic 
Shells.  —  Up  to  this  point  the  ordinary  distribution  of  mag- 
netism along  a  bar  has  been  the  only  distribution  considered. 
It  is  theoretically  possible  to  have  magnetism  distributed 
over  a  thin  sheet  so  that  the  whole  of  one  face  of  the  sheet 
shall  have  one  kind  of  magnetism,  and  the  other  face  the 
other  kind  of  magnetism ;  such  distribution  is,  however,  un- 


CH.  II.   121] 


MAGNETIC   FIGURES 


101 


stable.  If  an  immense  number  of  little  magnets  were  placed 
together  side  by  side,  like  the  cells  in  a  honey  eorjb;j  alt  wHh 
their  N-seeking  ends  upwards,  and  S-seeking  ends  down- 
wards, the  whole  of  one  face  of  the  slab  would  be  one  large 
flat  N-seeking  pole,  and  the  other  face  S-seeking.  Such  a 
distribution  as  this  over  a  surface  or  sheet  is  termed  a  la- 
mellar distribution,  to  distinguish  it  from  the  ordinary  dis- 
tribution along  a  line  or  bar,  which  is  termed,  for  distinction, 
the  solenoidal,  or  circuital,  distribution.  A  lamellarly  mag- 
netized magnet  is  sometimes  spoken  of  as  a  magnetic  shell. 
121.  Magnetic  Figures.  —  Gilbert  showed l  that  if  a 
sheet  of  paper  or  card  be  placed  over  a  magnet,  and  iron 
filings  are  dusted  over  the  paper,  they  settle  down  in  curv- 
ing lines,  forming  a  magnetic  figure,  the  general  form  of  which 
for  a  bar  magnet  is  shown  in  Fig.  69.  The  filings  should 
be  fine,  and  sifted 
through  a  bit  of  mus- 
lin ;  to  facilitate  their 
settling  in  the  lines, 
the  sheet  of  paper 
should  be  lightly 
tapped.  The  figures 
thus  obtained  can  be 
fixed  permanently  by 
several  processes. 
The  best  of  these  con- 
sists in  employing  a 
sheet  of  glass  which  has  been  previously  gummed  and  dried, 
instead  of  the  sheet  of  paper;  after  this  has  been  placed 
above  the  magnet  the  filings  are  sifted  evenly  over  the  sur- 
face, and  then  the  glass  is  tapped;  then  a  jet  of  steam  is 
caused  to  play  gently  above  the  sheet,  softening  the  surface 
of  the  gum,  which,  as  it  hardens,  fixes  the  filings  in  their 
places.  Inspection  of  the  figure  will  show  that  the  lines 
diverge  nearly  radially  from  each  pole,  and  curve  round  to 

1  The  magnetic  figures  were  known  to  Lucretius. 


FIG.  69.  —  Lines  of  Force  delineated  by  Iron  Filings. 


102 


ELECTRICITY   AND   MAGNETISM 


[PT.  i.  121 


FIG.  70.  —  Field  of  Horse-shoe 
Magnet. 


meet  these  from  the  opposite  pole.     Fig.  70,  produced  from 

a  horse-shoe  magnet,  shows  how  the  magnetic  field  is  most 

intense  between  the  poles,  but  spreads  beyond  them  in  wide 

curves.  Faraday,  who  made  a 
great  use  of  this  method  of  in- 
vestigating the  distribution  of 
magnetism  in  various  "  fields," 
gave  to  the  lines  the  name  of  lines 
of  force.  They  represent,  as 
shown  by  tfye  action  on  little 
magnetic  particles  which  set  them- 
selves thus  in  obedience  to  the 
attractions  and  repulsions  in  the 
field,  the  resultant  direction  of  the 
forces  at  every  point ;  for  each 
particle  tends  to  assume  the  direc- 
tion of  the  force  jointly  due  to 
the  simultaneous  action  of  both 

poles ;  hence  the  curves  of  filings  may  be  taken  to  represent 

visibly  the  invisible  lines  of  magnetic  force.1     Faraday  pointed 

out  that  these  "  lines  of  force  "  map 

out  the  magnetic  field,  showing  by 

their  position  the  direction  of  the 

magnetic  force,  and  by  their  number 

its  intensity.     If  a  small  N-seeking 

pole  could  be  obtained  alone,  and 

put  down  on  any  one  of  these  lines 

of  force,  it  would  tend  to  move  along 

that  line  from  N  to  S ;  a  single  S- 

seeking  pole  would  tend   to  move 

.          .  .  .  FIG.  71.  —  Field  of  a  Single  Pole. 

along  the  line  in  an  opposite  direc- 
tion.     In  Fig.   71,   which   is  the  field   about  one  end  of 
a  bar  magnet,  the  magnetic  lines  are  simply  radial.     Faraday 

1  Or  rather  the  component  part  of  the  magnetic  force  resolved  into  the 
plane  of  the  figure ;  which  is  not  quite  the  same  thing,  for  above  .the  poles 
the  filings  stand  up  nearly  vertically  to  this  plane. 


CH.  ii.  122,  123]         CONSEQUENT   POLES  103 

also  pointed  out  that  the  actions  of  attraction  or  repul- 
sion in  the  field  are  always  related  to  the  directions  in 
the  field  of  the  magnetic  lines.  He  assigned  to  these  lines 
of  force  certain  physical  properties  (which  are,  however, 
only  true  of  them  in  a  secondary  sense),  viz.,  that  they 
tend  to  shorten  themselves  from  end  to  end,  and  that  they 
repel  one  another  as  they  lie  side  by  side.  The  modern  way 
of  stating  the  matter  is,  that  in  every  magnetic  field  there 
are  certain  stresses,  consisting  of  a  tension  along  the  lines  of 
force,  and  a  pressure  across  them. 

122.  Consequent  Poles.  —  The  method  of  sprinkling 
filings  may  be  applied  to  ascertain  the  presence  of  consequent 
poles  in  a  bar  of  steel,  the  figure  obtained  resembling  that 
depicted  in  Fig.  72.  Such  a  state  of  things  is  produced  when 


FIG.  72.  —  Consequent  Poles. 

a  strip  of  very  hard  steel  is  purposely  irregularly  magnetized 
by  touching  it  with  strong  magnets  at  certain  points.  A 
strip  thus  magnetized  virtually  consists  of  several  magnets 
put  end  to  end,  but  in  reverse  directions,  NS,  SN,  etc.  Con- 
sequent poles  can  also  be  produced  in  an  electromagnet  by 
reversing  the  direction  in  which  the  wire  is  coiled  around 
part  of  the  core. 

123.  Fields  mapped  by  Filings.  —  The  forces  producing 
attraction  between  unlike  poles,  and  repulsion  between  like 
poles,  are  beautifully  illustrated  by  the  magnetic  figures 
obtained  in  the  fields  between  the  poles  in  the  two  cases,  as 
given  in  Figs.  73  and  74.  In  Fig.  73  the  poles  are  of  opposite 


104         ELECTRICITY   AND   MAGNETISM     [PT.  i.  124,  125 

kinds,  and  the  lines  of  force  curve  across  out  of  one  pole  into 
the  other;  while  in  Fig.  74,  which  represents  the  action  of 
two  similar  poles,  the  lines  of  force  curve  away  as  if  repelling 
one  another,  and  turn  aside  at  right  angles. 


FIG.  73.  —  Field  due  to  Opposite  FIG.  74.  —  Field  due  to  Similar 

Poles.  Poles. 


124.  Magnetic     Writing.  —  Another    kind    of    magnetic 
figures  was  discovered  by  De  Haldat,  who  wrote  with  the 
pole  of  a  magnet  upon  a  thin  steel  plate  (such  as  a  saw-blade) , 
and  then  sprinkled  filings  over  it.     The  writing,  which  is 
quite  invisible  in  itself,  comes  out  in  the  lines  of  filings  that 
stick  to  the  magnetized  parts ;   this  magic  writing  will  con- 
tinue in  a  steel  plate  many  months.     See  also  Art.  599  on 
the  Telegraphone. 

125.  Mechanical* Effects  of  Magnetization.  —  Joule  found 
an  iron  bar  to  increase  by  y^nnnr  °f  its  length  when  strongly 
magnetized.     Bidwell  found  that  with  still  stronger  mag- 
netizing forces  iron  contracts  again ;   and  rods  stretched  by 
a  weight  contract  more  when  magnetized  than  unstretched 
rods  do.     Barrett  observed  that  nickel  shows  a  slight  con- 
traction  when   magnetized.     These   are   proofs   that   mag- 
netization is   an   action  affecting  the   arrangement   of  the 
molecules.     This  supposition  is  confirmed  by  the  observa- 
tion of  Page,  that  at  the  moment  when  a  bar  is  magnetized 
or  demagnetized,  a  faint  metallic  clink  is  heard  in  the  bar. 
Sir  Wm.  Grove  showed  that  when  a  tube  containing  water 
rendered  muddy  by  stirring  up  in  it  finely-divided  magnetic 
oxide  of  iron  is  magnetized,  the  liquid  becomes  clearer  in  the 
direction  of  magnetization,  the  particles  apparently  setting 


CH.  ii.  126, 127]    EFFECTS   OF   MAGNETIZATION  105 

themselves  end-on,  and  allowing  more  light  to  pass  between 
them.  A  twisted  iron  wire  tends  to  untwist  itself  when 
magnetized.  A  piece  of  iron,  when  powerfully  magnetized 
and  demagnetized  in  rapid  succession,  grows  hot,  as  if  mag- 
netization were  accompanied  by  internal  friction  (Art.  395). 

126.  Action  of  Magnetism  on  Light.  —  Faraday  discovered 
that  a  ray  of  polarized  light  passing  through  certain  sub- 
stances in  a  powerful  magnetic  field  has  the  direction  of  its 
vibrations  changed.     This  phenomenon,  which  is  sometimes 
called  "  The  Magnetization  of  Light,"  is  better  described 
as  "  The  Rotation  of  the  Plane  of  Polarization  of  Light  by 
Magnetism."     The  amount  of  rotation  differs  in  different 
media,  and  varies  with  the  magnetizing  force.     A  ray  of 
polarized  light  is  also  rotated  by  reflexion  at  the  end  or  side 
of  a  powerful  magnet.     Further  mention  is  made  of  these 
discoveries  in  the  section  on  Electro-optics,  Arts.  611  to 
616,  p.  620. 

127.  The  Act  of  Magnetizing.  —  All  these  various  phe- 
nomena point  to  a  theory  of  magnetism  very  different  from 
the  old  notion  of  fluids.     It  appears 

that  every  particle  of  a  magnet  is 
itself  a  magnet,  and  that  the  magnet 


only  becomes  a  magnet  as  a  whole  FIG.  75.  —  Molecular  state  of 
by  the  particles  being  so  turned  as 

to  point  one  way.  The  act  of  magnetizing  consists  in  turn- 
ing the  molecules  more  or  less  into  one  particular  direction. 
If  a  glass  tube  full  of  iron  filings  is  magnetized,  the  filings 
can  be  seen  to  set  themselves  endways,  and  that,  when  thus 
once  set,  they  act  as  a  magnet  until  shaken  up.  It  appears 
to  be  harder  to  turn  the  individual  molecules  of  solid  steel 
than  those  of  soft  iron ;  but,  when  once  so  set,  they  remain 
end-on  unless  violently  struck  or  heated.  As  Weber,  who 
propounded  this  notion  of  molecular  magnetism,  pointed 
out,  it  follows  from  this  theory  that  when  all  the  particles 
are  turned  end-on  the  limits  of  possible  magnetization  would 
have  been  attained.  Some  careful  experiments  of  Beetz  on 


106  ELECTRICITY   AND   MAGNETISM       [FT.  i.  127 

iron  deposited  by  electrolysis  entirely  confirm  this  conclu- 
sion. Fig.  75  may  be  taken  to  represent  a  non-magnetized 
piece  of  iron  or  steel  in  which  the  arrangement  of  the  particles 
is  absolutely  miscellaneous,  in  little  groups :  they  do  not 
point  in  any  one  direction  more  than  another.  When  mag- 
netized slightly,  there  will  be  a  greater  percentage  pointing 
in  the  direction  of  the  magnetizing  force.  When  fully  mag- 
netized —  if  that  were  possible  —  they  would  all  point  in 
the  same  direction  as  in  Fig.  76. 

In  very  few  cases,  however,  is  the  magnetization  uniform 
throughout  the  whole  length  of  a  bar:    the  particles  are 

more  fully  completely 
turned  into  line  at  the 
middle  part  of  the  bar 
than  at  the  ends. 

If  the   intrinsic   mag- 
*'    '  ''  •'    '  *'    %i  %1  x%   "*     netization  of  the  steel  at 

FIG.  76.  —  Molecular  State  of  Magnetized  Bar.  ,. 

every  part  of  a  magnet 

were  equal,  the  free  poles  would  be  found  only  at  the  end 
surfaces ;  but  the  fact  that  the  free  magnetism  is  not  at  the 
ends  merely,  but  diminishes  from  the  ends  towards  the 
middle,  shows  that  the  intensity  of  the  intrinsic  magnetiza- 
tion must  be  less  towards  and  at  the  ends  than  it  is  at  the 
middle  of  the  bar.  In  Fig.  76  an  attempt  is  made  to  depict 
this.  It  will  be  noticed  that  the  magnetic  lines  run  through 
the  steel  and  emerge  into  the  air  in  curves.  Some  of  the 
lines  do  not  run  all  the  length  of  the  bar  but  leak  out  at  the 
sides.  If  the  bar  were  uniformly  magnetized  the  lines  would 
emerge  at  the  ends  only.  It  is  clear  that  the  middle  piece  is 
more  thoroughly  magnetized  than  any  other  part.  Mag- 
netism in  fact  consists  of  a  sort  of  grain  or  structure  con- 
ferred upon  the  steel.  Wherever  this  structure  comes  up  at 
a  surface,  there  the  surface  properties  of  magnetism  are 
found.  A  pole  is  simply  a  region  where  the  magnetic  lines 
pass  through  the  surface  of  the  steel  or  iron. 
The  optical  phenomena  led  Clerk  Maxwell  to  the  further, 


CH.  ii.  128,  129]     THEORY   OF  MAGNETIZATION  107 

conclusion  that  these  longitudinally-set  molecules  are  rotat- 
ing round  their  long  axes,  and  that  in  the  "  ether  "  of  space 
there  is  also  a  vortical  motion  along  the  magnetic  lines; 
this  motion,  if  occurring  in  a  perfect  medium  (as  the  "  ether  " 
may  be  considered),  producing  tensions  along  the  lines  of 
the  magnetic  field,  and  pressures  at  right  angles  to  them, 
would  afford  a  satisfactory  explanation  of  the  magnetic 
attractions  and  repulsions  which  apparently  act  across 
empty  space. 

128.  Magnetism  a  Form  of  Energy.  —  Though  we  speak 
freely  of  magnetic  "  force  "  and,  later  in  the  book,  of  mag- 
netic "  flux/'  it  should  be  pointed  out  that  the  magnetic 
field  represents  a  form  of  potential  energy,   and  that  in 
treating  it  as  a  flux  or  flow  of  intangible  agent  issuing  from 
a  N-seeking  pole  and  returning  into  a  S-seeking  pole,  we  are 
following  what  is  merely  a  convention  instituted  to  facili- 
tate calculations.     If  we  pull  a  N-seeking  pole  to  a  short 
distance  away  from  a  S-seeking  pole,  so  that  there  is  a  mag- 
netic field  between  them,  we  have  to  exert  force,  and  there- 
fore do  some  work  in  producing  that  field.     This  energy  we 
have  thus  expended  is  stored  up  as  potential  energy  in  the 
field.     When  a  piece  of  steel  is  magnetized  by  means  of  a 
magnet,   the  magnet  is  not  thereby  weakened ;    and  the 
necessary  energy  is  supplied  by  the  mechanical  effort  of  the 
person  who  applies  the  magnet. 

129.  Theory  of  Molecular  Magnetism.  —  The  magnetism 
of  iron  and  steel  is  intimately  connected  with  the  molecular 
rigidity  of  the  material.     Apparently  each  molecule  of  a 
magnetic  metal  has  an  absolutely  constant  inherent  mag- 
netic polarity.     When  a  piece  of  iron  or  steel  is  apparently 
neutral,  its  molecules  are  internally  arranged  so  as  to  satisfy 
each    other's    polarity,    forming    closed    magnetic    circuits 
amongst  themselves. 

Weber  supposed  that  there  was  in  hard  steel  some  sort  of 
friction  which  prevented  the  molecules  when  once  mag- 
netized from  turning  back  into  higgledy-piggledy  positions. 


108  ELECTRICITY   AND  MAGNETISM          [PT.  i.  130 

Ewing,  however,  showed  that  a  complete  explanation  was 
afforded  by  supposing  the  particles  to  be  subject  to  mutual 
forces.  In  any  group  not  subjected  to  an  external  mag- 
netizing force  the  particles  will  arrange  themselves  so  as  to 
satisfy  one  another's  polarity.  Of  the  possible  groupings  some 
are,  however,  unstable.  Four  possible  stable  groupings  of 
six  pivoted  needles  are  shown  in  Fig.  77.  Ewing  constructed 
a  model  consisting  of  a  large  number  of  pivoted  magnetic 


s  /       \  \ 

\     /     /       \    \    \ 
\/  \\ 


FIG.  77.  —  Molecular  Groupings  according  to  Ewing. 

needles  arranged  in  one  layer.  When  these  needles  were 
simply  agitated  and  allowed  to  come  to  rest  they  settled 
down  in  miscellaneous  groups ;  but  when  acted  upon  by  a 
gradually  increasing  magnetic  force  they  turned  round,  the 
operation  showing  three  stages  —  (i.)  with  very  small  mag- 
netizing force  the  needles  merely  turned  through  a  small 
angle;  (ii.)  when  a  certain  force  was  applied  the  groupings 
became  unstable,  some  of  the  needles  suddenly  swinging 
round  to  a  new  position,  with  the  result  that  the  majority 
of  the  needles  point  nearly  but  not  quite  along  the  direction 
of  the  force;  (iii.)  a  further  increase  of  the  magnetizing 
force  cannot  produce  much  more  effect ;  it  can  only  pull 
the  needles  a  little  more  perfectly  into  line.  All  these  things 
correspond  to  the  three  stages  observed  (see  Art.  391)  in  the 
gradual  magnetization  of  iron  or  steel. 

LESSON  XI.  —  Laws  of  Magnetic  Force 
130.    Laws  of  Magnetic  Force. 

FIRST  LAW.  —  Like  magnetic  poles  repel  one  another; 
unlike  magnetic  poles  attract  one  another. 


CH.  ii.  131]  LAWS   OF   MAGNETIC   FORCE  109 

SECOND  LAW.  —  The  force  exerted  between  two  mag- 
netic poles  is  proportional  to  the  product  of  their 
strengths,  and  is  inversely  proportional  to  the  square 
of  the  distance  between  them,  provided  that  the  dis- 
tance is  so  great  that  the  poles  may  be  regarded  as 
mere  points. 

131.  The  Law  of  Inverse  Squares.  —  The  second  of  the 
above  laws  is  commonly  known  as  the  law  of  inverse  squares; 
it  is  essentially  a  law  of  point-action,  and  is  not  true  for 
poles  of  elongated  or  extended  surface.  The  similar  law  of 
electrical  attraction  has  already  been  explained  and  illus- 
trated (Art.  19).  This  law  furnishes  the  explanation  of  a 
fact  mentioned  in  an  earlier  lesson,  Art.  95,  that  small  pieces 
of  iron  are  drawn  bodily  up  to  a  magnet  pole.  If  a  small 
piece  of  iron  wire,  a,  b  (Fig.  78),  be  suspended  by  a  thread, 
and  the  N-pointing  pole  A  of  a  magnet  be  brought  near  it, 
the  iron  is  thereby  induc- 
tively magnetized ;  it  turns 
round  and  points  towards 
the  magnet  pole,  setting 
itself  as  nearly  as  possible 
along  a  line  of  force,  its  near 

end  b  becoming  a  S-Seeking    FlG.  78._Magnetic  Force  on  Short  Needle 

pole,  and  its  farther  end  a 

becoming  a  N-seeking  pole.  Now  the  pole  b  will  be  attracted 
and  the  pole  a  will  be  repelled.  But  these  two  forces  do 
not  exactly  equal  one  another,  since  the  distances  are  un- 
equal. The  repulsion  will  (by  the  law  of  inverse  squares) 

be  proportional  to  ( .  0  •  and  the  attraction  will  be  pro- 
portional to  /A7N2.  Hence  the  bit  of  iron  a,  b  will  experience 

(Ao) 

a  pair  of  forces,  turning  it  into  a  certain  direction,  and  also 
a  total  force  drawing  it  bodily  toward  A.  Only  those  bodies 
are  attracted  by  magnets  in  which  magnetism  can  thus  be 


110  ELECTRICITY   AND   MAGNETISM    [PT.  i.  132,  133 

induced ;    and  they  are  attracted  only  because  of  the  mag- 
netism induced  in  them. 

We  mentioned,  Art.  95,  that  a  magnet  needle  floating 
freely  on  a  bit  of  cork  on  the  surface  of  a  liquid  is  acted 
upon  by  forces  that  give  it  a  certain  direction,  but  that, 
unlike  the  last  case,  it  does  not  tend  to  rush  as  a  whole 
either  to  the  north  or  to  the  south.  It  experiences  a  rota- 
tion, because  the  attraction  and  repulsion  of  the  magnetic 
poles  of  the  earth  act  in  a  certain  direction ;  but  since  the 
magnetic  poles  of  the  earth  are  at  a  distance  enormously 
great  as  compared  with  the  length  from  one  pole  of  the  float- 
ing magnet  to  the  other,  we  may  say  that,  for  all  practical 
purposes,  the  poles  of  the  magnet  are  at  the  same  distance 
from  the  N-pole  of  the  earth.  The  attracting  force  on  the 
N-pointing  pole  of  the  needle  is  therefore  practically  no 
greater  than  the  repelling  force  acting  on  the  S-pointing 
pole,  hence  there  is  no  motion  of  translation  given  to  the 
floating  needle  as  a  whole ;  it  is  directed,  not  attracted. 

132.  Measurement   of   Magnetic   Forces.  —  The   law   of 
inverse  squares  can  be  demonstrated  by  experiment.     But 
this  implies  that  we  .have  some  means  of  measuring  accurately 
the  amount  of  the  magnetic  forces  of  attraction  or  repulsion. 
Magnetic  force  may  be  measured  in  any  one  of  the  four 
following  ways :    (1)  by  observing  the  time  of  swing  of  a 
magnetic  needle  oscillating  under  the  influence  of  the  force 
(Art.  135) ;    (2)  by  observing  the  deflexion  it  produces  upon 
a  magnetic  needle  which  is  already  attracted  into  a  different 
direction  by  a  force  of  known  intensity  (Art.  133) ;    (3)  by 
balancing  it  against  the  torsion  of  an  elastic  thread  (Art. 
134) ;    (4)  by  balancing  it  against  the  force  of  gravity  as 
brought  into  play  in  attempting  to  deflect  a  magnet  hung 
by  two  parallel  strings  (called  the  bifilar  suspension),  for 
these  strings  cannot  be  twisted  out  of  their  parallel  position 
without  raising  the  centre  of  gravity  of  the  magnet. 

133.  Deflexion  Experiment.  —  Fig.  79  shows  an  apparatus 
in  which  a  compass-needle  can  be  deflected  by  one  pole  of  a 


CH.  ii.  134]  MEASUREMENT   OF   FORCE  111 

magnet  made  of  a  long  thin  bar  of  steel,  so  mounted  that 
its  upper  pole  is  always  over  the  centre  of  the  needle,  and 
therefore  has  no  tendency  to  turn  it.  So  set,  it  acts  as  a 
one-pole  magnet,  the  acting  pole  of  which 
can  be  placed  at  different  distances  from  the 
compass-needle.  It  is  found,  using  a  proper 
tangent  scale  (see  Art.  225)  for  the  compass- 
needle,  that  when  the  distance  is  doubled 
the  deflecting  force  is  reduced  to  one  quarter, 
and  so  forth.  See  Art.  130. 

134.    The    Torsion    Balance.  —  Coulomb 
applied  the  Torsion  Balance  to  the  measure-   FIG.  79.  —  Deflexion 

»  i  •      p  mi  •  •  by  one  Pole. 

ment  of  magnetic  forces.     The  main  princi- 
ples of  this  instrument  (as  used  to  measure  forces  of  electro- 
static repulsion)  were  described  on  p.  13.     Fig.  80  shows  how 
it  is  arranged  for  measuring  magnetic  repulsions. 

To  prove  1  the  law  of  inverse  squares,  Coulomb  made  the 
following  experiment :  —  The  instrument  was  first  adjusted 
so  that  a  magnetic  needle,  hung  in  a  copper  stirrup  to  the 
fine  silver  thread,  lay  in  the  magnetic  meridian  without  the 
wire  being  twisted.  This  was  done  by  first  putting  in  the 
magnet  and  adjusting  roughly,  then  replacing  it  by  a  copper 
bar  of  equal  weight,  and  once  more  adjusting,  thus  diminish- 
ing the  error  by  repeated  trials.  The  next  step  was  to  ascer- 
tain through  what  number  of  degrees  the  torsion-head  at 
the  top  of  the  thread  must  be  twisted  in  order  to  drag  the 
needle  1°  out  of  the  magnetic  meridian.  In  the  particular 
experiment  cited  it  was  found  that  35°  of  torsion  corresponded 
to  the  1°  of  deviation  of  the  magnet ;  then  a  magnet  was  in- 
troduced through  the  lid,  that  pole  being  downwards  which 

1  This  is  the  common  way  of  stating  the  matter ;  but  what  Coulomb 
really  tested  was  whether  his  magnet  poles  acted  as  points.  Had  they  acted 
exactly  as  if  the  magnetism  was  concentrated  at"  points,  the  geometric 
condition  of  the  law  of  inverse  squares  could  not  but  have  been  fulfilled. 
Robison  showed  that  if  a  steel  needle  is  provided  with  two  little  soft  iron 
spheres  on  its  ends,  the  effective  poles  are  exactly  at  the  centres  of  the 
spheres. 


112 


ELECTRICITY  AND   MAGNETISM          [PT.  i.  134 


repelled  the  pole  of  the  suspended  needle.  It  was  found 
(in  this  particular  experiment)  to  repel  the  pole  of  the  needle 
through  24°.  From  the  preliminary  trial  we  know  that  this 
directive  force  corresponds  to  24°  X  35°  of  the  torsion-head, 
and  to  this  we  must  add  the  actual  torsion  on  the  wire,  viz. 
the  24°,  making  a  total  of  864°,  which  we  will  call  the  "  tor- 


FIG.  80.  —  Magnetic  Torsion  Balance. 

sion  equivalent  "  of  the  repelling  force  when  the  poles  are 
thus  24°  apart.  Finally,  the  torsion-head  was  turned  round 
so  as  to  twist  the  suspended  magnet  round,  and  force  it 
nearer  to  the  fixed  pole,  until  the  distance  between  the  re- 
pelling poles  was  reduced  to  half  what  it  was  at  first.  It 
was  found  that  the  torsion-head  had  to  be  turned  round  8 
complete  rotations  to  bring  the  poles  to  12°  apart.  These 
8  rotations  were  an  actual  twist  of  8°  X  360°,  or  2880°. 
But  the  bottom  of  the  torsion  thread  was  still  twisted  12° 
as  compared  with  the  top,  the  force  producing  this  twist 


CH.  ii.  135]          METHOD    OF    OSCILLATIONS  113 

corresponding  to  12  X  35  (or  420°)  of  torsion ;  and  to  these 
the  actual  torsion  of  12°  must  be  added,  making  a  total  of 
2880°  +  420°  +  12°  =  3312.  The  result  then  of  halving 
the  distance  between  the  magnet  poles  was  to  increase  the 
force  fourfold,  for  3312  is  very  nearly  four  times  864.  Had 
the  distance  between  the  poles  been  reduced  to  one-third  the 
force  would  have  been  nine  times  as  great. 

We  may  also,  assuming  this  law  proved,  employ  the 
balance  to  measure  the  strengths  of  magnet  poles  by  measur- 
ing the  forces  they  exert  at  known  distances. 

135.  Method  of  Oscillations.1  —  If  a  magnet  suspended 
by  a  fine  thread,  or  poised  upon  a  point,  be  pushed  aside 
from  its  position  of  rest,  it  will  vibrate  backwards  and  for- 
wards, performing  oscillations  which,  although  they  gradually 
decrease  in  amplitude,  are  executed  in  very  nearly  equal 
times.  In  fact,  they  follow  a  law  similar  to  that  of  the  oscil- 
lations executed  by  a  pendulum  swinging  under  the  influence 
of  gravity.  The  law  of  pendular  vibrations  is,  that  the 
square  of  the  number  of  oscillations  executed  in  a  given  time  is 
proportional  to  the  force.  Hence  we  can  measure  magnetic 
forces  by  counting  the  oscillations  made  in  a  minute  by  a 
magnet.  It  must  be  remembered,  however,  that  the  actual 
number  of  oscillations  made  by  any  given  magnet  will  depend 
on  the  weight  of  the  magnet  and  on  its  leverage  around  its 
centre,  as  well  as  upon  the  strength  of  its  poles,  and  on  the 
intensity  of  the  field  in  which  it  may  be  placed  (see  calcula- 
tions, Art.  388). 

We  can  use  this  method  to  compare  the  intensity  of  the 
force  of  the  earth's  magnetism  2  at  any  place  with  that  at 
any  other  place  on  the  earth's  surface,  by  oscillating  a  mag- 
net at  one  place  and  then  taking  it  to  the  other  place  and 

1  It  is  possible,  also,  to  measure  electrical  forces  by  a  "method  of  oscil- 
lations" ;    a  small  charged  ball  at  the  end  of  a  horizontally-suspended  arm 
being  caused  to  oscillate  under  the  attracting  force  of  a  charged  conductor 
near  it,  whose  "force"  at  that  distance  is  proportional  to  the  square  of  the 
number  of  oscillations  in  a  given  time. 

2  Or,  more  strictly,  of  its  horizontal  component. 

I 


114  ELECTRICITY  AND   MAGNETISM          [PT.  i.  136 

oscillating  it  there.  If,  at  the  first,  it  makes  a  oscillations 
in  one  minute,  and  at  the  second  b  oscillations  a  minute, 
then  the  magnetic  forces  at  the  two  places  will  be  to  one 
another  in  the  ratio  of  a2  to  b2. 

Again,  we  may  use  the  method  to  compare  the  force 
exerted  at  any  point  by  a  magnet  near  it  with  the  force  of 
the  earth's  magnetism  at  that  point.  For,  if  we  swing  a 
small  magnetic  needle  there,  and  find  that  it  makes  m  oscil- 
lations a  minute  under  the  joint  action  1  of  the  earth's  mag- 
netism, and  that  of  the  neighbouring  magnet,  and  that, 
when  the  magnet  is  removed,  it  makes  n  oscillations  a  minute 
under  the  influence  of  the  earth's  magnetism  alone,  then  m2 
will  be  proportional  to  the  joint  forces,  n2  to  the  force  due 
to  the  earth's  magnetism,  and  the  difference  of  these,  or 
m2  —  n2  will  be  proportional  to  the  force  due  to  the  neigh- 
bouring magnet. 

136.    Surface    Distribution.  —  We    will    now    apply    the 
method  of  oscillations  to  measure  the  relative  quantities  of 
j        surface  magnetism  at  different  points  along  a 
i4--—  i     Jon     kar  magnet.     The  magnet  to  be  examined  is 
^P     set  up  vertically  (Fig.  81).     A  small  magnet, 
capable  of  swinging  horizontally,  is  brought 
near  it  and  set  at  a  short  distance  away  from 
4-  --  its  extremity,  and  then  oscillated,  while  the 

rate  of  its  oscillations  is  counted.  Suppose 
the  needle  were  such  that,  when  exposed  to 
the  earth's  magnetism  alone,  it  would  perform 
3  complete  oscillations  a  minute,  and  that, 
when  vibrating  at  its  place  near  the  end  of  the 

FIG.  81.  —  Surface  ,       •  ...  -ii     ,      i  -,       ,• 

Distribution  of   vertical  magnet  it  oscillated  14  times  a  minute, 


Magnetism.  tnen     ^     £Qrce    due    t()     the    magnet 

proportional   to  142  -  32  =  196  -  9  =  187.     Next,  let  the 
oscillating  magnet  be  brought  to  an  equal  distance  opposite 

1  We  are  here  assuming  that  the  magnet  is  so  placed  that  its  force  is  in 
a  line  with  that  of  the  earth's  magnetism  at  the  point,  and  that  the  other 
pole  of  the  magnet  is  so  far  away  as  not  to  affect  the  oscillating  needle. 


CH.  ii.  136]          DISTRIBUTION   OF   SURFACE  115 

a  point  a  little  away  from  the  end  of  the  vertical  magnet.  If, 
here,  it  oscillated  12  times  a  minute,  we  know  that  the  force 
will  be  proportional  to  122  -  32  =  144  -  9  =  135.  So  we 
shall  find  that  as  the  force  falls  off  the  oscillations  will 
be  fewer,  until,  when  we  put  the  oscillating  magnet  oppo- 
site the  middle  of  the  vertical  magnet,  we  shall  find  that  the 
number  of  oscillations  is  3  per  minute,  or  that  the  earth's 
force  is  the  only  force  affecting  the  oscillations.  In  Fig.  81 
we  have  indicated  the  number  of  oscillations  at  succes- 
sive points,  as  14,  12,  10,  8,  6,  5,  4,  and  3.  If  we  square 
these  numbers  and  subtract  9  from  each,  we  shall  get 
for  the  forces  at  the  various  points  the  following :  — 187, 


\ 


IN 


FIG.  82.  —  Exploration  by  Oscillations. 

135,  91,  55,  27,  16,  7,  0.  These  forces  may  be  taken 
to  represent  the  strength  of  the  free  magnetism  at  the 
various  points,  and  it  is  convenient  to  plot  them  out  graphi- 
cally in  the  manner  shown  in  Fig.  82,  where  the  heights  of 
the  dotted  lines  are  chosen  to  a  scale  to  represent  propor- 
tionally the  forces.  The  curve  which  joins  the  tops  of  these 
ordinates  shows  graphically  how  the  force,  which  is  greatest 
at  the  end,  falls  off  toward  the  middle.  On  a  distant  mag- 
net pole  these  forces,  thus  represented  by  this  curvilinear 
triangle,  would  act  as  if  concentrated  at  a  point  in  the 
magnet  opposite  the  "  centre  of  gravity  "  of  this  triangle  ; 
or,  in  other  words,  the  "  pole,"  which  is  the  centre  of  the 


116  ELECTRICITY  AND   MAGNETISM    [PT.  i.  137,  138 

resultant  forces,  is  not  at  the  end  of  the  magnet.  In  thin 
bars  of  magnetized  steel  it  is  at  about  TV  of  the  magnet's 
length  from  the  end. 

Another  way  to  explore  the  surface  distribution  is  to  take 
a  small  spherical  or  ellipsoidal  bullet  of  iron,  and  to  hang 
it  by  a  wire  to  a  spring  balance.  The  force  required  to 
detach  such  a  bit  of  iron  from  various  parts  of  the  surface 
of  a  magnet  may  be  taken  as  a  measure  of  the  distribution, 
the  forces  being  approximately  proportional  to  the  square 
of  the  surface  density. 

137.  Magnetic  Moment.  —  It  is  found  that  the  tendency 
of  a  magnet  to  turn  or  to  be  turned  by  another  magnet 
depends  not  only  on  the  strength  m  of  its  poles,  but  the 
length  I  between  them.     The  product  of  these  two  quantities 
m  X  Z  is  called  the  magnetic  moment  of  the  magnet,  and  is 
sometimes  denoted  by  the  symbol  M.     As  the  exact  position 
of  a  magnet's  poles  are  often  unknown,  it  is  easier  to  deter- 
mine M  than  to  measure  either  m  or  I  separately. 

138.  Method   of    Deflexions.  —  There   are   a  number  of 
ways  in  which  the  deflexion  of  a  magnet  by  another  magnet 
may  be  made  use  of  to  measure  magnetic  forces.1     We  can- 
not here  give  more  than  a  glance  at  first  principles.     When 
two  equal  and  opposite  forces  act  on  the  ends  of  a  rigid  bar 
they  simply  tend  to  turn  it  round.     Such  a  pair  of  forces 
form  what  is  called  a  "  couple,"  and  the  torque,  or  tendency 
to  turn  (formerly  called  the  "  moment  "  of  the  couple),  is 
obtained  by  multiplying  one  of  the  two  forces  by  the  per- 
pendicular distance  between  the  directions  of  the  forces. 
Such  a  couple  tends  to  produce  a  motion  of  rotation,  but 
not  a  motion  of  translation.     Now  a  magnetic  needle  placed 
in  a  magnetic  field  across  the  lines  of  force  experiences  a 
torque,  tending  to  rotate  it  round  into  the  magnetic  merid- 
ian, for  the  N-seeking  pole  is   urged   northwards,  and   the 

1  The  student  desirous  of  mastering  these  methods  of  measuring  mag- 
netic forces  should  consult  Professor  Andrew  Gray's  Absolute  Measurements 
in  Electricity  and  Magnetism. 


CH.  ii.  138] 


METHOD   OF   DEFLEXIONS 


117 


Wi— t 


FIG.  83.  —  Force-couple. 


S-seeking  pole  is  urged  southwards,  with  an  equal  and  op- 
posite force.  The  force  acting  on  each  pole  is  the  product  of 
the  strength  of  the  pole  and  the 
intensity  of  the  "  field,"  that  is 
to  say,  of  the  horizontal  com- 
ponent of  the  force  of  the  earth's 
magnetism  at  the  place.  We 
will  call  the  strength  of  the  N- 
seeking  pole  m;  and  we  will  use 
the  symbol  H  to  represent  the 
force  which  the  earth's  magnet- 
ism would  exert  in  a  horizontal 
direction  on  a  unit  of  magnetism. 
(The  value  of  H  is  different  at 
different  regions  of  the  globe.) 
The  force  on  the  pole  A  (see 
Fig.  83)  will  be  then  ra  X  H, 
and  that  on  pole  B  will  be  equal  and  opposite.  We  take 
NS  as  the  direction  of  the  magnetic  meridian :  the  forces 
will  be  parallel  to  this  direction.  Now,  the  needle  AB  lies 
obliquely  in  the  field,  while  the  magnetic  force  acting  on  A 
is  in  the  direction  of  the  line  PA,  and  that  on  B  in  the  direc- 
tion QB,  as  shown  by  the  arrows.  PQ  is  the  perpendicular 
distance  between  these  forces ;  hence  the  "  moment  "  of 
the  couple,  or  torque,  will  be  got  by  multiplying  the 
length  PQ  by  the  force  exerted  on  one  of  the  poles.  Using 
the  symbol  Y  for  the  torque,  we  may  write 

Y  =  PQ  X  m  •  H. 

But  PQ  is  equal  to  the  length  of  the  magnet  multiplied  by 
the  sine  1  of  the  angle  AOR,  which  is  the  angle  of  deflexion, 
and  which  we  will  call  5.  Hence,  using  I  for  the  length 
between  the  poles  of  the  magnet,  we  may  write  the  expres- 
sion for  the  moment  of  the  couple, 
Y  =  mlR  •  sin  5. 

1  If  any  reader  is  unacquainted  with  trigonometrical  terms  he  should  consult 
the  note  at  the  end  of  this  lesson,  on  "Ways  of  Reckoning  Angles,"  p.  127. 


118  ELECTRICITY   AND   MAGNETISM          [PT.  i.  139 

In  words  this  is :  the  torque  acting  on  the  needle  is  pro- 
portional to  its  "  magnetic  moment  "  (m  X  /),  to  the  hori- 
zontal force  of  the  earth's  magnetism,  and  to  the  sine  of  the 
angle  of  deflexion. 

The  reader  will  not  have  failed  to  notice  that  if  the  needle 
were  turned  more  obliquely,  the  distance  PQ  would  be 
longer,  and  would  be  greatest  if  the  needle  were  turned 
round  east-and-west,  or  in  the  direction  EW.  Also  the 
torque  tending  to  rotate  the  magnet  will  be  less  and  less  as 
the  needle  is  turned  more  nearly  into  the  direction  NS. 

139.  Law  of  Tangents.  —  Now,  let  us  suppose  that  the 
deflexion  5  were  produced  by  a  magnetic  force  applied  at 
right  angles  to  the  magnetic  meridian,  and  tending  to  draw 
the  pole  A  in  the  direction  RA.  The  length  of  the  line  RT 
multiplied  by  the  new  force  will  be  the  leverage  of  the  new 
couple  tending  to  twist  the  magnet  into  the  direction  EW. 
Now,  if  the  needle  has  come  to  rest  in  equilibrium  between 
these  two  forces,  it  is  clear  that  the  two  opposing  twists  are 
just  equal  and  opposite  in  power,  or  that  the  torque  due  to 
one  couple  is  equal  to  that  of  the  other  couple.  Hence  the 
force  in  the  direction  WE  will  be  to  the  force  in  the  direction 
SN  in  the  same  ratio  as  PQ  is  to  RT  or  as  PO  is  to  RO. 

Or,  calling  this  force  /, 

/:H  =  PO:RO. 
Or  /=Hg 

But  PO  =  AR,  and  ^  =  tan  6,  hence 
/  =  H  tan  5 ; 

or,  in  other  words,  the  magnetic  force  which,  acting  at  right 
angles  to  the  meridian,  produces  on  a  magnetic  needle  the  de- 
flexion 8,  is  equal  to  the  horizontal  force  of  the  earth's  mag- 
netism at  that  point,  multiplied  by  the  tangent  of  the  angle  of 
deflexion.  Hence,  also,  two  different  magnetic  forces  acting 
at  right  angles  to  the  meridian  would  severally  deflect  the 
needle  through  angles  whose  tangents  are  proportional  to 


CH.  ii.  140] 


MAGNETOMETERS 


119 


the  forces.     (See  the  Table  of  Tangents  of  Angles  on  page 
648.) 

This  very  important  theorem  is  applied  in  the  construc- 
tion of  certain  galvanometers  (see  Art.  225,  p.  192). 

140.  Magnetometers.  —  The  name  Magnetometer  is  given 
to  any  magnet  specially  arranged  as  an  instrument  for  the 
purpose  of  measuring  magnetic  forces. 
The  methods  of  observing  the  absolute 
values  of  magnetic  forces  in  dyne-units 
(units  in  the  "  C.G.S."  system)  will  be 
explained  in  Art.  388  at  the  end  of 
Lesson  XXVII.  Very  simple  magnet- 
ometers, consisting  of  small  needles 
pivoted,  or  suspended  by  a  fibre,  are 
commonly  used  for  measuring  the  rela- 
tive values  of  magnetic  forces.  One 
very  sensitive  form  (Fig.  84),  to  be 
used,  like  the  reflecting  galvanometer 
(Art.  228),  with  a  beam  of  light  as  a 
pointer,  consists  of  a  small  thin  silvered  glass  mirror,  a 
half-inch  or  less  in  diameter,  having  two  or  three  very  light 
magnets  cemented  at  its  back,  suspended  by  a  single  thread 
of  cocoon  silk,  and  enclosed  in  a  suitable  case.  Another 
useful  form  (Fig.  85)  consists  of  a  short  compass-needle 
poised  on  a  pivot  having  a  light  index  of  aluminium  long 
enough  to  move  over  a  scale  divided  into  tangent  values 
(see  Art.  225). 

A  convenient  deflexion  magnetometer  for  comparing  the 
magnetic  moments  (Art.  137)  of  two  magnets  is  afforded  by 
such  a  tangent  compass  placed  in  the  middle  of  a  graduated 
n  platform  (Fig.  86).     There  are 

two    methods    of    using    this 
apparatus. 

First  Position:  End-on 
Method.  —  The  platform  being 
set  to  lie  magnetically  east  and  west,  the  deflecting  magnet 


FIG.  84.  —  Magnetometer. 


FIG.  85.  —  Magnetometer  Needle. 


120  ELECTRICITY   AND   MAGNETISM          [PT.  i.  140 

is  set  end-on.  In  these  circumstances  the  force  is  found  to 
vary  directly  as  the  magnetic  moment  (Art.  137),  and  ap- 
proximately inversely  as  the  cube  of  the  distance  between  the 
centres  of  the  magnets,  or,  in  symbols, — 

/=  2M/r3. 

This  formula  is  deduced  as  follows.  Let  the  half-length  of 
the  deflecting  magnet  be  called  J  /,  and  let  the  strength  of 
either  pole  of  the  magnet  be  called  m,  and  let  r  be  the  dis- 


S 

FIG.  86.  —  End-on  Position. 

tance  of  the  centre  of  the  magnet  from  the  compass  needle. 
Then  if  a  unit  pole  were  situated  at  the  compass  centre,  its 
distance  from  the  nearer  pole  of  the  deflecting  magnet  would 
be  r  —  %l,  and  from  the  further  pole  would  be  r  -f  |/.  Hence, 
applying  the  law  of  inverse  squares,  the  resultant  force  on  the 
Unit  pole  at  the  centre  would  be  the  difference  between  the 
two  forces  m/(r  —  J/)2  and  m/(r  -f-  |Q2,  which  equals 

2lmr 


r4  - 

So  that,  if  r  is  great  compared  with  |/,  we  may  write  as  an 
approximation, 

2lmr      ,  .  .    .    2M 

— — >  which  is  — T-* 

r4  r3 

But  we  have  seen  above  that  where  magnetic  force  is  meas- 
ured by  a  deflexion  6  at  a  place  where  the  H  is  earth's 
horizontal  magnetic  force,  /  is  equal  to  H  tan  8  ;  so  that 

2M/r3  =  H  tan  6, 
whence 

M  =    7-3H  tan  6. 


CH.  ii.  141,  142]      UNIT   POLE    STRENGTH  121 

Second  Position :  Broadside  on.  —  The  platform  being 
turned  into  the  north-south  position,  the  deflecting  magnet 
is  set  broadside-on  (see  Fig.  87).  In  this  case  the  magnet 
deflects  the  needle  in  the  other  direction  and  with  half  the 
force  that  it  would  have  exerted  at  an  equal 
distance  in  the  end-on  position.  But  the 
force  still  varies  approximately  as  the  inverse 
cube  of  the  distance ;  the  formula  being  now 


20 

or,  if  \l  is  small  compared  with  r} 

f=  M/r3, 

whence  VV 

M  =  r3H  tan  5. 


141.  Balance  Methods.  —  In  either  posi- 
tion   of    the    magnetometer   platform    two 
magnets  can  be  placed  on  the  two  sides  of 
the  board  so  as  to  balance  one  another's 
effects   by   adjusting   them  to   proper   dis- 
tances.    This  gives  a  comparison  of  their 
magnetic  moments  in  terms  of  their  respec- 
tive distances,  or 

FIG.  87.  —  Broad- 
Mi  I  M2  =   Ti3  :  r23.  side-on  Position. 

142.  Unit  Strength  of  Pole.— The  Second  Law  of   Mag- 
netic Force  (see  Art.  130,  p.  109)  stated  that  the  force  exerted 
between  two  poles  was  proportional  to  the  product  of  their 
strengths,  and  was  inversely  proportional  to  the  square  of  the 
distance  between  them.     It  is  possible  to  choose  such  a 
strength  of  pole  that  this  proportionality  shall  become  nu- 
merically an  equality.     In  order  that  this  may  be  so,  we 
must  adopt  the  following  as  our  unit  of  strength  of  a  pole,  or 
unit  magnetic  pole :    A  Unit  Magnetic  Pole  is  one  of  such  a 
strength  that,  when  placed  at  a  distance  of  one  centimeter  from 
a  similar  pole  of  equal  strength  it  repels  it  with  a  force  of  one 
dyne  (see  Art.  379,  p.  340).     If  we  adopt  this  definition  we 


122  ELECTRICITY   AND   MAGNETISM  [PT.  i.  143 

may  express  the  second  law  of  magnetic  force  in  the  follow- 
ing equation :  — 

,      m  X  m' 

/=   ~dT 

where  /  is  the  force  (in  dynes),  m  and  m'  the  strengths  of 
the  two  poles,  and  d  the  distance  between  them  (in  centi- 
metres). From  this  definition  is  derived  the  arbitrary  con- 
vention about  magnetic  lines.  .  If  at  any  place  in  a  magnetic 
field  we  imagine  a  unit  magnetic  pole  to  be  set  it  will  be  acted 
upon,  tending  to  move  along  the  lines  of  the  field.  The  force 
exerted,  per  unit  of  magnetism  (i.e.  /-£•  m)  is  a  measure  of 
the  strength  of  the  field ;  so  that  §  =  /  -T-  m,  and  /  =  §w. 
Then  if  at  that  place  we  find  the  force  on  unit  pole  to  be  § 
dynes,  we  may  conceive  that  there  are  §  lines  drawn  per 
square  centimetre.  For  example,  if  we  describe  the  field  as 
having  50  lines  side  by  side  per  square  centimetre,  we  mean 
that  a  unit  pole  placed  there  will  be  acted  on  with  a  force  of 
50  dynes.  Or  we  may  say  simply  :  the  intensity  of  the  field 
is  50  dynes  per  unit  pole,  or  the  flux  density  is  50  gausses  (see 
Art.  365,  p.  327). 

143.  Theory  of  Magnetic  Figures.  —  We  saw  (Art.  121) 
that  magnetic  figures  are  produced  by  iron  filings  setting 
themselves  in  certain  directions  in  the  field  of  force  around  a 
magnet.  We  can  now  apply  the  law  of  inverse  squares  to  aid 
us  in  determining  the  direction  in  which  a  filing  will  set  itself 
at  any  point  in  the  field.  Let  NS  (Fig.  88)  be  a  long  thin 
magnet,  and  P  any  point  in  the  field  due  to  its  magnetism. 
If  the  N-seeking  pole  of  a  small  magnet  be  put  at  P,  it  will  be 
attracted  by  S  and  repelled  by  N;  the  directions  of  these 
two  forces  will  be  along  the  lines  PS  and  PN.  The  amounts 
of  the  forces  may  be  represented  by  certain  lengths  marked 
out  along  these  lines.  Suppose  the  distance  PN  is  twice  as 
great  as  PS,  the  repelling  force  along  PN  will  be  J  as  strong  as 
the  attracting  force  along  PS.  So  measure  a  distance  out, 
PA  towards  S  four  times  as  long  as  the  length  PB  measured 
along  PN  away  from  N.  Find  the  resultant  force  in  the 


CH.  ii.  144]         SUPERPOSITION   OF   FIELDS  123 

usual  way  of  compounding  mechanical  forces,  by  completing 
the  parallelogram  PARE  ;  the  diagonal  PR  represents  by  its 
length  and  direction  the  magnitude  and  the  direction  of  the 
resultant  magnetic  force  at  the  point  P.  In  fact  the  line 
PR  represents  the  line  along  which  a  small  magnet  or  an 
iron  filing  would  set  itself.  In  a  similar  way  we  might  ascer- 
tain the  direction  of  the  lines  of  force  at  any  point  of  the  field. 
The  little  arrows  in  Fig.  88  show  how  the  lines  of  force  start 


\ 


flfrllllllllllliii^ 


\ 


FIG.  88.  —  Theory  of  Magnetic  Curves. 

out  from  the  N-pole  and  curve  round  to  meet  in  the  S-pole. 
The  student  should  compare  this  figure  with  the  lines  of  filings 
of  Fig.  69  (p.  101).  Henceforth  we  must  think  of  every 
magnet  as  being  permeated  by  these  magnetic  lines  which 
extend  out  into  the  surrounding  space.  The  whole  number 
of  magnetic  lines  which  run  through  a  magnet  is  termed  its 
magnetic  flux  (Art.  364).  It  must  be  remembered,  in  making 
such  experimental  curves,  that  they  are  liable  to  be  distorted 
by  the  presence  of  the  earth's  magnetic  field. 

144.  Superposition  of  Magnetic  Fields.  —  The  process  of 
finding  resultants  used  above  may  be  generalized  for  the 
study  of  the  superposition  of  magnetic  fields.  When  the 
lines  of  force  of  two  separate  magnetic  fields  are  separately 
drawn,  and  then  superposed,  they  present  varied  patterns 


124 


ELECTRICITY   AND   MAGNETISM      [PT.  i.  144 


of  intersecting  lines.  Fig.  89  represents  such  a  case.  The 
lines  of  the  resultant  field  formed  by  the  superposition  of 
these  two  fields  may  be  drawn  with  sufficient  accuracy  by 
merely  joining  the  diagonals  of  the  little  quadrilaterals, 
regard  being  had  to 
the  initial  directions 
of  the  separate  fields 
to  decide  which  of 
the  two  diagonals 
(as  in  the  corner 
sketches)  shall  be 
drawn.  As  ex- 
amples of  this  plan 
of  super-position  are 
given  Fig.  90  a  and 
Fig.  906,  represent- 
ing respectively  the 
field  between  two  equal  poles  of  opposite  kinds,  and  two 
equal  poles  of  the  same  kind.  They  should  be  compared 
with  Figs.  73  and  74,  p.  104.  The  same  principle  is  used 


FIG.  89.  —  Superposition  of  Magnetic  Fields. 


FIG.  90«.  —  Field  due  to  two  Poles  of  opposite  kinds. 

in  Figs.  220  and  221,  pp.  387,  388,  for  ascertaining  the  result- 
ant magnetic  field  between  two  wires  carrying  currents,  and 
in  Fig.  190  for  drawing  the  resultant  field  when  a  wire  carrying 


CH.  ii.  145]       ACTION   OF   OPPOSITE    POLES  125 

a  current  is  placed  between  the  poles  of  a  magnet.  The 
superposition  of  two  electric  fields  (Art.  420,  p.  387)  can  be 
graphically  treated  in  the  same  way. 


FIG.  90  6.  —  Field  due  to  two  Poles  of  similar  kinds. 

145.  Neutralizing  Action  of  Opposite  Poles.  —  That  poles 
of  opposite  name  can  neutralize  one  another  may  be  shown 
by  the  familiar  experiment  of  hanging  a  steel  ring  or  key  to 
the  N-pole  of  a  bar  magnet.  On  bringing  the  S-pole  of 
another  bar  magnet  to  touch  the  first,  the  two  poles  will 
neutralize  each  other's  actions,  and  the  ring  or  key  will  drop. 

A  Magnetic  Paradox.  —  If  the  N-seeking  pole  of  a  strong 
magnet  be  held  at  some  distance  from  the  N-seeking  pole 
of  a  weak  magnet,  it  will  repel  it ;  but  if  it  is  pushed  up  quite 
close  it  will  be  found  now  to  attract  it.  This  paradoxical 
experiment  is  explained  by  the  fact  that  the  magnetism  in- 
duced in  the  weak  magnet  by  the  powerful  one  will  be  of  the 
opposite  kind,  and  will  be  attracted  ;  and  when  the  powerful 
magnet  is  near,  this  induced  magnetism  may  overpower  and 
mask  the  original  magnetism  of  the  weak  magnet.  The 
student  must  be  cautioned  that  in  most  of  the  experiments  on 
magnet  poles  similar  perturbing  causes  are  at  work.  The 
magnetism  in  a  magnet  is  not  quite  fixed,  but  is  liable  to  be 
disturbed  in  its  distribution  by  the  near  presence  of  other 
magnet  poles,  for  no  steel  is  so  hard  as  not  to  be  temporarily 


126 


ELECTRICITY   AND   MAGNETISM 


[PT.  i.  145 


affected  by  magnetic  induction.     For  instance,  it  is  possible 
for  the  polarity  of  a  compass  needle  to  be  accidentally,  or 


purposely,  reversed  by  suddenly  bringing  a  powerful  magnet 
close  to  it ;  the  magnetism  being  reversed  by  influence  before 
the  steel  needle  has  had  time  to  turn  round. 


CH.  ii.  146-148]     RECKONING  OF  ANGLES  127 

146.  Pull  of  Permanent  Magnets  at  Varying  Distances. — 
When  a  permanent  magnet  is  in  contact  with  its  keeper,  the 
whole  flux  of  magnetic  lines  goes  through  the  keeper  and 
pulls  it  (Fig.  91  a).     But  if  the  keeper  be  removed  to  a  short 
distance,  though  the  total  number  of  lines  of  the  magnet  is 
unaltered,  the  pull  is  smaller  because  now  a  part  only  of  the 
flux  passes  through  the  keeper,  as  in  Fig.  91  b  and  c.     The 
greater  the  width  of  the  air-gap,  the  fewer  the  number  of 
lines  that  reach  the  keeper.     The  pull  does  not  vary  inversely 
as  the  square  of  the  distance. 

NOTE  ON  WAYS  OF  RECKONING  ANGLES  AND 
SOLID  ANGLES 

147.  Reckoning  in  Degrees.  —  When  two  straight  lines  intersect 
one  another  they  form  an  angle  between  them  ;  and  this  angle  may 
be  defined  as  the  amount  of  rotation  which 

one  of  the  lines  has  performed  round  a  fixed 
point  in  the  other  line.  Thus  we  may  sup- 
pose the  line  CP  in  Fig.  92  to  have  originally 
lain  along  CO,  and  then  turned  round  to  its  IBO{ 
present  position.  The  amount  by  which  it 
has  been  rotated  is  clearly  a  certain  fraction 
of  the  whole  way  round ;  and  the  amount  of 
rotation  round  C  we  call  "  the  angle  which  PC 
makes  with  OC,"  or  more  simply  "the  angle 

PCO."  But  there  are  a  number  of  different  ways  of  reckoning  this 
angle.  The  common  way  is  to  reckon  the  angle  by  "  degrees  "  of  arc. 
Thus,  suppose  a  circle  to  be  drawn  round  C,  if  the  circumference  of 
the  circle  were  divided  into  360  parts  each  part  would  be  called 
"one  degree"  (1°),  and  the  angle  would  be  reckoned  by  naming  the 
number  of  such  degrees  along  the  curved  arc  OP.  In  the  figure  the 

arc  is  about  5?i°,  or  — ^  of  the  whole  way  round,  no  matter  what 
ooO 

size  the  circle  is  drawn. 

148.  Reckoning  in  Radians.  —  A  more  sensible  but  less  usual  way 
to  express  an  angle  is  to  reckon  it  by  the  ratio  between  the  length  of 
the  curved  arc  that  "subtends"  the  angle  and  the  length  of  the 
radius  of  the  circle.     Suppose  we  have  drawn  round  the  centre  C  a 
circle  whose  radius  is  one  centimetre,  the  diameter  will  be  two  cen- 
timetres.    The  length  of  the  circumference  all  round  is  known  to 


128 


ELECTRICITY   AND   MAGNETISM 


[PT.  i.  149 


be  about  3f  times  the  length  of  the  diameter,  or  more  exactly 
3*14159  .  .  .  This  number  is  so  awkward  that,  for  convenience, 
we  always  use  for  it  the  Greek  letter  IT.  Hence  the  length  of  the  cir- 
cumference of  our  circle,  whose  radius  is  one  centimetre,  will  be 
6'28318  .  .  .  centimetres,  or  2?r  centimetres.  We  can  then  reckon 
any  angle  by  naming  the  length  of  arc  that  subtends  it  on  a  circle 
one  centimetre  in  radius.  If  we  choose  the  angle  PCO,  such  that  the 
curved  are  OP  shall  be  just  one  centimetre  long,  this  will  be  the  angle 
one,  or  unit  of  angular  measure,  or,  as  it  is  sometimes  called,  the 
angle  PCO  will  be  one  "  radian."  In  degree-measure  one  radian 

Q  £*f\O 

=    —  —  =  57°  17'  nearly.     All  the  way  round  the  circle  will  be  2ir 


radians. 


A  right  angle  will  be  -  radians. 


149.  Reckoning  by  Sines  or  Cosines.  —  In  trigonometry  other 
ways  of  reckoning  angles  are  used,  in  which,  however,  the  angles 
themselves  are  not  reckoned,  but  certain  "  functions  "  of  them, 
called  "  sines,"  "  cosines,"  "  tangents,"  etc.  For  readers  not 

accustomed    to   these  we  will    briefly  explain 

the  geometrical  nature  of  these  "  functions." 

Suppose     we     draw      (Fig. 

93).   our    circle    as    before 

round  centre   C,   and   then 

drop     down     a    plumb-line 

PM,    on    to    the    line    CO; 
FIG.  93;  we  may,  instead  of  reckon- 

ing the  angle  by  the  curved 

arc,  reckon  it  by  the  length  of  the  line  PM.  It  is  clear  that  if  the 
angle  is  small  PM  will  be  short  ;  but  as  the  angle  opens  out  towards 
a  right  angle,  PM  will  get  longer  and  longer  (Fig.  94).  The  ratio  be- 
tween the  length  of  this  line  and  the  radius  of  the  circle  is  called  the 
,"  sine  "  of  the  angle,  and  if  the  radius  is  1  the  length  of  PM  will  be  the 
value  of  the  sine.  It  can  never  be  greater  than  1,  though  it  may  have 
all  values  between  1  and  —  1.  The  length  of  the  line  CM  will  also 
depend  upon  the  amount  of  the  angle.  If  the  angle  is  small  CM 
will  be  nearly  as  long  as  CO  ;  if  the  angle  open  out  to  nearly  a  right 
angle  CM  will  be  very  short.  The  length  of  CM  (when  the  radius 
is  1)  is  called  the  "  cosine  "  of  the  angle.  If  the  angle  be  called  0, 
then  we  may  for  shortness  write  these  functions  : 

PM 
sine  =         - 


cos  0 


CM. 

CP' 


CH.  ii.  150,  151] 


SOLID   ANGLES 


129 


150.  Reckoning  by  Tangents.  —  Suppose  we  draw  our  circle 
as  before  (Fig.  95),  but  at  the  point  O  draw  a  straight  line  touching 
the  circle,  the  tangent  line  at  O  ;  let  us  also 
prolong  CP  until  it  meets  the  tangent  line  at  T. 
We  may  measure  the  angle  between  OC  and 
CP  in  terms  of  the  length  of  the  tangent  OT  as 
compared  with  the  length  of  the  radius.  Since 
our  radius  is  1,  this  ratio  is  numerically  the 
length  of  OT,  and  we  may  therefore  call  the 
length  of  OT  the  "  tangent  "  of  the  angle  OCP. 
It  is  clear  that  smaller  angles  will  have  smaller 
tangents,  but  that  larger  angles  may  have  very 
large  tangents  ;  in  fact,  the  length  of  the  tangent 
when  PC  was  moved  round  to  a  right  angle 
would  be  infinitely  great.  It  can  be  shown  that 
the  ratio  between  the  lengths  of  the  sine  and  of  the  cosine  of  the 
angle  is  the  same  as  the  ratio  between  the  length  of  the  tangent 
and  that  of  the  radius ;  or  the  tangent  of  an  angle  is  equal  to  its 
sine  divided  by  its  cosine.  The  formula  for  the  tangent  may  be 
written : 

TO        PM 


FIG.  95. 


tan  6  = 


OC        MC' 


r 


A  table  of  radians,  sines,  tangents,  etc.,  is  given  at  the  end  of 
this  book  as  Appendix  A,  p.  648. 

151.  Solid  Angles.  —  When  three 
or  more  surfaces  intersect  at  a  point 
they  form  a  solid  angle:  there  is  a 
solid  angle,  for  example,  at  the  top 
of  a  pyramid,  or  of  a  cone,  and  one 
at  every  corner  of  a  diamond  that  has 
been  cut.  If  a  surface  of  any  given 
shape  be  near  a  point,  it  is  said  to  sub- 
tend a  certain  solid  angle  at  that 
point,  the  solid  angle  being  mapped  out  by  drawing  lines  from  all 
points  of  the  edge  of  this  surface  to  the  point  P  (Fig.  96).  An 
irregular  cone  will  thus  be  generated  whose  solid  angle  is  the  solid 
angle  subtended  at  P  by  the  surface  EF.  To  reckon  this  solid 
angle  we  adopt  an  expedient  similar  to  that  adopted  when  we 
wished  to  reckon  a  plane  angle  in  radians.  About  the  point  P, 
with  radius  of  1  centimetre,  describe  a  sphere,  which  will  intercept 
the  cone  over  an  area  MN :  the  area  thus  intercepted  measures  the 
solid  angle.  If  the  sphere  have  the  radius  1,  its  total  surface  is  4^. 
The  solid  angle  subtended  at  the  centre  by  a  hemisphere  would  be 


FIG.  96. 


130  ELECTRICITY  AND   MAGNETISM          [PT.  i.  152 

2ir.  The  ratio  between  the  area  of  the  surface  EF  and  the  area  of 
the  surface  MN  is  the  ratio  between  the  squares  of  the  lines  EP 
and  MP.  The  solid  angle  subtended  at  a  point  by  a  given  sur- 
face (other  things  being  equal)  is  inversely  proportional  to  the 
square  of  the  distance  of  that  surface  from  the  point.  This  is  the 
basis  of  the  law  of  inverse  squares. 

LESSON  XII.  —  Terrestrial  Magnetism 

152.  The  Mariners'  Compass.  —  It  was  mentioned  in 
Art.  89,  p.  83,  that  the  compass  sold  by  opticians  consists 
of  a  magnetized  steel  needle  balanced  on  a  fine  point  above 


FIG.  97.  —  Mariners'  Compass,  with  Sights. 

a  card  marked  out  N,  S,  E,  W,  etc.     The  Mariners'  Compass 
is,  however,  somewhat  differently  arranged. 

In  Fig.  97  one  of  the  forms  of  a  Mariners'  Compass,  used 
for  nautical  observations,  is  shown.  Here  the  card,  divided 
into  the  32  "  points  of  the  compass,"  is  itself  attached  to  the 
needle,  and  swings  round  with  it  so  that  the  point  marked 
N  on  the  card  always  points  to  the  magnetic  north.  The 
bowl  containing  the  compass  is  swung  on  gimbals  to  keep  it 
level  when  the  ship  rolls  or  pitches.  The  iron  hull  and  iron 
fittings  of  ships  affect  the  compass,  which  has  therefore  to  be 


CH.  ii.  153,  154]         MARINERS'    COMPASS 


131 


corrected  by  placing  correcting  masses  of  iron  near  it,  or  by 
fixing  it  high  upon  a  mast.  The  error  of  the  compass  due  to 
the  magnetism  of  the  ship  itself  is  called  the  deviation. 


FIG.  98.  —  Kelviu  Compass  Card. 

153.  Lord  Kelvin's  Compass.  —  Lord  Kelvin  introduced 
many  improvements.     To  reduce  friction  on  the  pivot,  and 
to  make  the  horizontal  oscillations  of  the  card  slow,   he 
reduced  the  weight,  making  the  card  light  by  cutting  away 
the  middle  part,  and  substituting  for  the  usual  long  heavy 
needle  a  set  of  six  or  eight  short  light  steel  needles  slung  by 
silk  threads  below  the  card.     A  10-inch  card  with  its  needles 
weighs  only  180  grains  (11J  grammes).     To  damp  the  swing- 
ing of  the  bowl  it  was  partly  filled  with  stiff  castor  oil.     The 
shortness  of  the  needles  enabled  corrections  to  be  made  for 
the  deviation. 

154.  Floating   Compasses.  —  Recently  a   further  step   has 
been  taken  by  filling  the  entire  compass  with  liquid,  which 
helps  to  buoy  up  the  card  and  reduce  its  effective  weight 
on  the  pivot.     Fig.  99  shows  a  section  of  the  Kelvin-Chet- 
wynd  compass,  from  which  the  way  in  which  the  float  is 


132 


ELECTRICITY   AND   MAGNETISM 


[PT.  i.  155 


attached  below  the  compass  card  may  be  seen.  The  weight 
of  card  and  float  is  actually  82-9  grammes;  but,  being 
buoyed  up  by  the  spirit  in  which  it  is  immersed,  the  actual 
weight  on  the  pivot  is  only  7  grammes.  Fig.  100  depicts  the 
compass  complete  in  its  binnacle.  The  card  is  illuminated 


FIG.  99.  —  Kelvin-Chetwynd  Compass. 

by  two  lamps,  and  is  viewed  by  an  optical  contrivance  so  that 
the  card  itself  appears  vertical. 

155.  Correction  of  Compass  Errors.  —  The  iron  hull  of  a 
ship  is  always  magnetic ;  there  is  a  permanent  part  of  the 
magnetism  depending  on  the  direction  in  which  she  lay  when 
being  built,  and  a  temporary  part  due  to  the  earth  inducing 
in  her  a  temporary  polarity  which  varies  according  to  the 
direction  in  which  she  is  heading.  There  is  a  third  error, 
called  the  heeling  error,  due  to  the  vertical  component  of 
the  magnetism,  which,  when  a  ship  rolls,  or  heels  over,  tends 
to  set  the  compass  swinging.  The  permanent  part  of  the 
ship's  magnetism  manifests  itself  by  causing  the  deviation, 
while  the  ship  is  "  swung  "  right  round,  to  become  a  maxi- 
mum twice ;  hence  it  is  called  the  semicircular  error.  The 
temporary  or  induced  part  causes  the  deviation  to  become 
a  maximum  four  times  while  the  ship  is  swung  round  ;  hence 


CH.  ii.  150] 


ERRORS   OF   THE    COMPASS 


133 


it  is  called  the  quadrantal  error.  The  semicircular  error  is 
compensated  by  putting  below  the  compass  two  horizontal 
sets  of  correcting  steel  magnets  :  one  set  fixed  fore  and  aft  to 
correct  the  error  that  is  found  when  the  ship's  head  lies  east 
or  west;  the  other  set  is  fixed 
athwart-ships  to  compensate  the 
error  when  the  ship's  head  points 
north  or  south.  A  third  group  of 
steel  magnets  is  set  vertically  to 
correct  the  heeling  error.  The 
quadrantal  error  is  corrected  by 
placing  two  large  balls  of  soft  iron 
at  the  sides  of  the  compass, 
athwart-ship,  to  correct  for  the 
masses  of  iron  of  the  hull  which 
lie  fore  and  aft.  They  must  be  of 
suitable  size  and  be  set  at  suitable 
distances  apart.  In  Fig.  100  the 
two  spherical  correctors  are  seen 
supported  right  and  left  of  the 
compass.  It  was  impossible  to 
correct  the  quadrantal  error  when 
long  heavy  needles  were  used  for 
the  compass  prior  to  Lord  Kelvin's 
improvements.  As  the  vertical 
component  of  the  earth's  magnetism  varies  from  one  part  of 
the  earth's  surface  to  another  (Art.  158),  a  further  correc- 
tion for  errors  due  to  this  is  made  by  placing  under  the 
compass  a  vertical  soft-iron  bar,  called,  from  its  inventor, 
a  Flinders  bar. 

156.  The  Earth's  Poles.  —  Gilbert  made  the  great  dis- 
covery that  the  compass-needle  points  north  and  south 
because  the  earth  is  itself  also  a  great  magnet.  The  magnetic 
poles  of  the  earth  are,  however,  not  exactly  at  the  geographi- 
cal north  and  south  poles.  The  magnetic  north  pole  of  the 
earth  i^  more  than  1000  miles  away  from  the  actual  pole. 


FIG.  100.  —  Kelvin-Chetwynd 
Compass. 


134 


ELECTRICITY  AND   MAGNETISM 


[PT.  i.  157 


In  1831  it  was  found  by  Sir  J.  C.  Ross  to  be  situated  in 
Boothia  Felix,  just  within  the  Arctic  Circle,  being  in  lat. 
70°  5'  N.,  and  long.  96°  46'  W.  The  south  magnetic  pole 
of  the  earth  was  reached  in  1909  by  Sir  Ernest  Shackleton's 
expedition.  It  is  situated  in  lat.  72°  25'  S.,  long.  155°  16'  E. 
157.  Declination.  —  In  consequence  of  this  natural  dis- 
tribution the  compass-needle  does  not  at  all  points  of  the 
earth's  surface  point  truly  north  and  south.  Thus,  in  1894, 
the  compass-needle  at  London  pointed  at  an  angle  of  about 
17°  west  of  the  true  north;  in  1910  it  was  16°  5'.  This 
angle  between  the  magnetic  meridian  l  and  the  geographical 
meridian  of  a  place  is  called  the  magnetic  Declination  of  that 

place.  The  existence  of  this 
declination  was  discovered 
by  Columbus  in  1492,  but 
may  have  been  previously 
observed.  The  fact  that  the 
declination  differs  at  differ- 
ent points  of  the  earth's 
surface,  is  the  undisputed 
discovery  of  Columbus. 

In  order  that  ships  may 
steer  by  the  compass,  mag- 
netic charts  (Art.  161,  p. 
138)  must  be  prepared,  and 
the  declination  at  different 
places  accurately  measured. 
The  upright  pieces,  P,  P', 
on  the  "  azimuth  compass" 
drawn  in  Fig.  97,  are  for  the  purpose  of  sighting  a  star  whose 
position  may  be  known  from  astronomical  tables,  and  thus 
affording  a  comparison  between  the  magnetic  meridian  of 

1  The  Magnetic  Meridian  of  any  place  is  an  imaginary  plane  drawn 
through  the  zenith,  and  passing  through  the  magnetic  north  point  and 
magnetic  south  point  of  the  horizon,  as  observed  at  that  place  by  the  point- 
ing of  a  horizontally-suspended  compass-needle. 


FIG.  101.  —  Dipping-Needle. 


CH.  ii.  158] 


DIPPING-NEEDLE 


135 


the  place  and  the  geographical  meridian,  and  of  measuring  the 
angle  between  them. 

158.  Inclination  or  Dip.  —  Norman,  an  instrument-maker, 
discovered  in  1576  that  a  balanced  needle,  when  magnetized, 
tends  to  dip  downwards  toward  the  north.  He  therefore  con- 
structed a  Dipping-Nee  die,  capable  of  turning  in  a  vertical 
plane  about  a  horizontal  axis,  with  which  he  found  the  dip  to  be 
(at  London)  an  angle  of  71°  50'.  A  simple  form  of  dipping- 
needle  is  shown  in  Fig.  101.  The  dip-circles  used  in  the 
magnetic  observatory  at  Kew  are  much  more  exact  and 
delicate  instruments.  It  was,  however,  found  that  the  dip, 
like  the  declination,  differs  at  different  parts  of  the  earth's 
surface,  and  that  it  also  undergoes  changes  from  year  to 
year.  The  dip  in  London  for  the  year  1910  was  66°  59'; 
in  1915  it  is  about  66°  55'.  In  1910  it  was  70°  5'  at  Edin- 
burgh, and  70°  45'  at  Aberdeen.  At  the  north  magnetic 
pole  the  needle  dips  straight  down.  The  following  Table 
gives  particulars  of  the  Declination,  Inclination,  and  hori- 
zontal magnetic  intensity  at  a  number  of  important  places, 
the  values  being  approximately  true  for  the  year  1910. 

TABLE  OF  MAGNETIC  DECLINATION  AND  INCLINATION 
(for  Year  1910) 


LOCALITY 

DECLINATION 

DIP 

HORIZONTAL 
FOBCE  H 

London  (Greenwich)     .     .     . 
London  (Kew)     

15°  41'  W. 
16°    5'  W. 

66°  57'  N. 
66°  59'  N. 

0-1851 
0*1850 

Toronto  (Agincourt)     .     .     . 
Washington  (Cheltenham)     . 
Paris 

5°  59'  W. 
5°  36'  W. 
14°  20'  W 

74°  40'  N. 
70°  31'  N. 
64°  53'  N 

0-1630 
Q'1990 
0"1998 

Pavlovsk    .                .          . 

1°  22'  E 

70°  39'  N 

0*1648 

Potsdam     
Athens 

9°    3'  W. 

4°  35'  W 

66°  21'  N. 
52°  11'  N 

0-1881 
0"2620 

Hong-Kong     

0°    1'  E 

30°  59'  N 

0"3706 

Rio  Janeiro 

9°  31'  W 

14°  25'  S 

0*2473 

Bombay  (Alibag)      .... 
Mauritius 

0°  59'  E. 
9°  31'  \\r 

23°  35'  N. 
53°  37'  S 

0-3684 
0*2330 

Tokio      .     .     . 

4°  58'  W 

49°    7'  N 

0*3001 

Christchurch  (New  Zealand) 

16°  37'  E. 

67°  59'  S. 

0-2251 

136  ELECTRICITY   AND   MAGNETISM          [FT.  i.  159 

159.  Intensity.  —  Three  things  must  be  known  in  order 
to  specify  exactly  the  magnetic  conditions  at  any  place; 
these  three  elements  are  : 

The  Declination  ; 

The  Inclination  or  Dip  ;   and 

The  Intensity  of  the  Magnetic  Force. 

The  magnetic  force  is  measured  by  one  of  the  methods 
mentioned  in  the  preceding  Lesson.  Its  direction  is  in  the 
line  of  the  dipping-needle,  which,  like  every  magnet,  tends 
to  set  itself  along  the  lines  of  force.  It  is,  however,  more 
convenient  to  measure  the  force  not  in  its  total  intensity  in 
the  line  of  the  dip,  but  to  measure  the  horizontal  component 
of  the  force,  —  that  is  to  say,  the  force  in  the  direction  of 
the  horizontal  compass-needle,  from  which  the  total  force 
can  be  calculated  if  the  dip  is  known.1  If  in  the  triangle  of 
H  Fig.  102,  the  horizontal  line  H  is  drawn  to 

scale  to  represent  by  its  length  the  horizontal 
component  of  the  earth's  magnetic  force,  and 
the  vertical  line  V,  the  vertical  component 
of  the  force,  then  the  oblique  line  I  will  repre- 
sent the  total  force  down  the  line  of  dip; 
and  the  angle  0  between  H  and  I  will  be  the 
angle  of  dip.  If  the  horizontal  and  vertical 
FIG  102  —  Compo-  components  of  the  force  are  known,  the  total 


of    Earth's  force  and  the  angle  of  the  dip  can  both  be 

Magnetic   Force. 

calculated.2  The  horizontal  component  of 
the  force,  or  "  horizontal  intensity,"  can  be  ascertained  either 
by  the  method  of  Vibrations  or  by  the  method  of  Deflexions. 
The  mean  horizontal  force  of  the  earth's  magnetism  at  London 
in  1915  is  0*1848  gausses,  the  mean  vertical  force  0*4332,  the 
total  force  (in  the  line  of  dip)  was  0'4710  gausses.  The  dis- 
tribution of  the  magnetic  force  at  different  points  of  the  earth's 

1  For  if  H  =  Horizontal  Component  of  Force,  and  I  =  Total  Force,  and 
0  -  Angle  of  Dip,  I  =  H  •*•  cos  0. 

2  For  H2  +  V2  =  I2,  where  V  =  Vertical  Component  of  Force. 


CH.  ii.  160] 


MAGNETIC   INTENSITY 


137 


surface  is  irregular,  and  varies  in  different  latitudes  accord- 
ing to  an  approximate  law,  which,  as  given  by  Biot,  is  that 
the  force  is  proportional  to  V 1  -f-  3  sin2/,  where  I  is  the  mag- 
netic latitude. 


160.  Kew  Pattern  Magnetometer.  —  For  the  precise 
measurement  of  the  declination  and  of  the  horizontal  force 
a  magnetometer  of  fine  construction  is  employed,  as  shown 
in  Fig.  103.  The  magnets  are  small  hollow  cylinders  which 
can  be  suspended  in  order  to  observe  their  times  of  oscilla- 


138  ELECTRICITY  AND   MAGNETISM          [PT.  i.  161 

tion,  and  which  can  also  be  placed  on  supports  M  at  known 
distances  on  a  cross  bar  XY,  to  serve  as  deflecting  magnets 
in  an  end-on  position.  The  tubular  magnets  are  provided 
with  a  scale  S  at  one  end,  and  a  lens  at  the  other  to  facilitate 
observation.  Art.  140  gives  the  method  of  calculating 
from  such  observations  the  value  of  H  at  the  place  of 
observation. 

161.  Magnetic  Maps.  —  For  purposes  of  convenience  it 
is  usual  to  construct  magnetic  maps,  on  which  such  data  as 
those  given  in  the  Table  on  p.  135  can  be  marked  down. 
Such  maps  may  be  constructed  in  several  ways.  Thus,  it 
would  be  possible  to  take  a  map  of  England,  or  of  the  world, 
and  mark  it  over  with  lines  such  as  to  represent  by  their 
direction  the  actual  direction  in  which  the  compass  points ; 
in  fact  to  draw  the  lines  of  force  or  magnetic  meridians.  A 
more  useful  way  of  marking  the  map  is  to  find  out  those 
places  at  which  the  declination  is  the  same,  and  to  join 
these  places  by  a  line.  The  Magnetic  Map  of  Great  Britain, 
which  forms  the  Frontispiece  to  these  Lessons,  is  constructed 
on  this  plan  from  the  magnetic  survey  lately  made  by 
Rticker  and  Thorpe  as  corrected  by  the  latest  observations 
of  Kew  Observatory  and  of  the  Admiralty.  At  Plymouth 
the  compass-needle  in  1910  pointed  17°  to  the  west  of  the 
geographical  north.  The  declination  at  Bristol  and  at  Dur- 
ham was  in  this  year  the  same  as  at  Plymouth.  Hence  a 
line  joining  these  towns  may  be  called  a  line  of  equal  declina- 
tion) or  an  Isogonic  line.  It  will  be  seen  from  this  map  that 
the  declination  is  greater  in  the  north-west  of  England  than 
in  the  south-east.  We  might  similarly  construct  a  magnetic 
map,  marking  it  with  lines  joining  places  where  the  dip  was 
equal :  such  lines  would  be  called  Isoclinic  lines.  In  Eng- 
land ,they  run  across  the  map  from  west-south-west  to  east- 
north-east.  For  example,  in  1910  the  needle  dipped  about 
68°  at  Nottingham  and  at  Aberystwyth.  Through  these 
places  then  the  isoclinic  of  68°  may  be  drawn  for  that  epoch. 
On  the  globe  the  isogonic  lines  run  for  the  most  part  from 


CH.  ii.  162]  MAGNETIC   MAPS  139 

the  north  magnetic  pole  to  the  south  magnetic  polar  region, 
but,  owing  to  the  irregularities  of  distribution  of  the  earth's 
magnetism,  their  forms  are  not  simple.  The  isoclinic  lines 
of  the  globe  run  round  the  earth  like  the  parallels  of  latitude, 
but  are  irregular  in  form.  Thus  the  line  joining  places  where 
the  north-seeking  pole  of  the  needle  dips  down  70°  runs 
across  Scotland  and  the  north  of  Ireland;  then  crosses  the 
Atlantic  in  a  south-westerly  direction,  traverses  the  United 
States,  swerving  northwards,  and  just  crosses  the  southern 
tip  of  Alaska.  It  drops  somewhat  southward  again  as  it 
crosses  China,  but  again  curves  northwards  as  it  enters 
Russian  territory.  Finally  it  crosses  the  southern  part  of 
the  Baltic,  and  reaches  Scotland  across  the  German  Ocean. 
The  magnetic  chart  of  the  United  States,  which  is  also  given 
at  the  front  of  this  book,  is  for  the  year  1910.  It  has  been 
prepared  from  data  furnished  by  Dr.  L.  A.  Bauer  of  the 
U.S.  Geodetic  Survey.  It  will  be  noticed  that  in  the  year 
1910  the  magnetic  declination  was  zero  at  Pittsburg  (Ohio), 
and  near  Charleston  (S.  Carolina). 

The  line  passing  through  places  of  no  declination  is  called 
the  agonic  line.  It  passes  across  both  hemispheres,  crossing 
Russia,  Persia,  and  Australia.  There  is  another  agonic  line 
in  eastern  Asia  enclosing  a  region  around  Japan,  within 
which  there  is  a  westerly  declination. 

162.  Variations  of  Earth's  Magnetism. —  We  have  already 
mentioned  that  both  the  declination  and  the  inclination 
are  subject  to  changes;  some  of  these  changes  take  place 
very  slowly,  others  occur  every  year,  and  others  again 
every  day. 

Those  changes  which  require  many  years  to  run  their 
course  are  called  secular  changes. 

The  variations  of  the  Declination  previous  to  1580  are 
not  recorded;  the  compass  at  London  then  pointed  11°  east 
of  true  north.  This  easterly  declination  gradually  decreased, 
until  in  1657  the  compass  pointed  true  north.  It  then 
moved  westward,  attaining  a  maximum  of  24°  27 '  about 


140 


ELECTRICITY  AND   MAGNETISM 


[PT.  i.  162 


the  year  1816,  from  which  time  it  has  slowly  diminished  to 
its  present  value  (15°  19 '  in  1915) ;  it  diminishes  (in  Eng- 
land) at  about  the  rate  of  9'  per  year.  At  about  the  year 
1976  it  will  again  point  truly  north,  making  a  complete 
cycle  of  changes  in  about  640  years. 

The  Inclination  in  1576  was  71°  50',  and  it  slowly  increased 
till  1720,  when  the  angle  of  dip  reached  the  maximum  value 
of  74°  42'.  It  has  since  steadily  diminished  to  its  present 
(1915)  value  of  66°  55'.  The  period  in  which  the  cycle  is 
completed  is  not  known,  but  the  rate  of  variation  of  the  dip 
is  less  at  the  present  time  than  it  was  fifty  years  ago.  In  all 
parts  of  the  earth  both  declination  and  inclination  are  slowly 
changing.  The  following  table  gives  the  data  of  the  secular 
changes  at  London. 

TABLE  OF  SECULAR  MAGNETIC  VARIATIONS 


YEAB 

DECLINATION 

INCLINATION 

1576 

71°  50' 

1580 

11°  17'  E. 

1600 

72°    0' 

1622 

6°  12' 

1634 

4°0' 

1657 

0°  0'  min. 

1676 

3°  0'  W. 

73°  30' 

1705 

9°0' 

1720 

13°  0' 

74°  42'  max. 

1760 

19°  30' 

1780 

72°  8' 

1800 

24°  6' 

70°  35' 

1816 

24°  30'  max. 

1830 

24°  2' 

69°  3' 

1855 

23°  0' 

1868 

20°  33' 

68°  2' 

1878 

19°  14' 

67°  43' 

1880 

18°  40' 

67°  40' 

1890 

17°  26' 

67°  23' 

1900 

16°  16' 

67°  9' 

1910 

15°  3' 

66°  56' 

1920 

14°  20' 

66°  49' 

CH.  ii.  163-165]       MAGNETIC   VARIATION  141 

The  Total  Magnetic  force,  or  "  Intensity,"  also  slowly 
changes  in  value.  As  measured  near  London,  it  was  equal 
to  0-4791  gausses  in  1848,  0'4740  in  1866,  in  1880  0'4736 
gausses,  in  1890  Q'4741.1  In  1915  it  is  0'4710.  Owing  to 
the  steady  decrease  of  the  angle  at  which  the  needle  dips, 
the  horizontal  component  of  this  force  (i.e.  the  "  Horizontal 
Intensity  ")  is  slightly  increasing.  It  was  0*1716  gausses  in 
1814,  0-1797  gausses  at  the  beginning  of  1880,  and  0'1823 
gausses  in  1890.  In  1915  it  is  0'1848. 

163.  Daily    Variations.  —  Both    compass    and     dipping- 
needle,  if  minutely  observed,  exhibit  slight  daily  motions. 
About  7  A.M.  the  compass-needle  begins  to  travel  westward 
with  a  motion  which  lasts  till  about  1  P.M.  ;  during  the  after- 
noon and  evening  the  needle  slowly  travels  back  eastward, 
until  about  10  P.M.  ;  after -this  it  rests  quiet ;  but  in  summer- 
time the  needle  begins  to  move  again  slightly  to  the  west  at 
about  midnight,  and  returns  again  eastward  before  7  A.M. 
These  delicate  variations  —  never  more  than  10'  of  arc  — 
appear  to  be  connected  with  the  position  of  the  sun;    and 
the  moon  also  exercises  a  minute  influence  upon  the  position 
of  the  needle. 

164.  Annual  Variations.  —  There  is  also  an  annual  varia- 
tion corresponding  with  the  movement  of  the  earth  around 
the  sun.     In  the  British  Islands  the  total  force  is  greatest  in 
June  and  least  in  February,  but  in  the  Southern  Hemi- 
sphere, in  Tasmania,  the  reverse  is  the  case.     The  dip  also 
differs  with  the  season  of  the  year,  the  angle  of  dip  being  (in 
England)  less  during  the  four  summer  months  than  in  the 
rest  of  the  year. 

165.  Eleven-Year    Period.  —  General    Sabine    discovered 
that  there  is  a  larger  amount  of  variation  of  the  declination 
occurring  about  once  every  eleven  years.     Schwabe  noticed 
that   the   recurrence   of  these   periods   coincided  with   the 
eleven-year  periods  at  which  there  is  a  maximum  of  spots  on 

1  That  is  to  say,  a  north  magnet  pole  of  unit  strength  is  urged  in  the 
line  of  dip,  with  a  mechanical  force  of  a  little  less  than  half  a  dyne. 


142  ELECTRICITY  AND   MAGNETISM    [PT.  i.  166-168 

the  sun.  Professor  Balfour  Stewart  and  others  have  en- 
deavoured to  trace  a  similar  periodicity  in  the  recurrence  of 
aurorae 1  and  of  other  phenomena. 

166.  Magnetic  Storms.  —  It  is  sometimes  observed   that 
a  sudden   (though  very  minute)  irregular  disturbance  will 
affect  the  whole  of  the  compass-needles  over  a  considerable 
region  of  the  globe.     Such  occurrences  are  known  as  mag- 
netic storms;    they  frequently  occur  at  the  time  when  an 
aurora  is  visible.     It  is  suggested  that  they  are  due  to  the 
emission  by  the  sun  of  invisible  radiations  resembling  kath- 
ode rays,  which  alter   the    conductivity  of    strata    of    the 
upper  air,  and  thus  augment  the  electric  currents  that  circu- 
late in  the  atmosphere. 

167.  Self-recording  Magnetic  Apparatus.  —  At   Kew  and 
other  magnetic  observatories  the  daily  and  hourly  variations 
of  the  magnet  are  recorded  on  a  continuous  register.     The 
means  employed  consists  in  throwing  a  beam  of  light  from 
a  lamp  on  to  a  light  mirror  attached  to  the  magnet  whose 
motion  is  to  be  observed.     A  spot  of  light  is  thus  reflected 
upon  a  ribbon  of  photographic  paper  prepared  so  as  to  be 
sensitive  to  light.     The  paper  is  moved  continuously  forward 
by  a  clockwork  train ;  and  if  the  magnet  be  at  rest  the  dark 
trace  on  the  paper  will  be  simply  a  straight  line.     If,  how- 
ever, the  magnet  moves  aside,  the  spot  of  light  reflected  from 
the  mirror  will  be  displaced,  and  the  photographed  line  will 
be   curved   or   crooked.     Comparison   of   such    records,    or 
magnetographs,  from  stations  widely  apart    on    the  earth's 
surface,  promises  to  afford  much  light  upon  the  cause  of 
the  changes  of  the  earth's  magnetism,  to  which  hitherto  no 
reliable  origin  has  been  with  certainty  assigned.     Schuster 
has  shown  that  these  changes  generally  come  from  without, 
and  not  from  within. 

168.  Theory  of  Earth's  Magnetism.  —  The  phenomenon 
of  earth-currents,  observed  to  occur  spontaneously  in  long 
telegraph  lines,  and  flowing  generally  in  directions  from  the 

1  See  Lesson  XXV.,  on  Atmospheric  Electricity  (p.  320). 


CH.  ii.  168]  MAGNETIC   STORMS  143 

poles  towards  the  Equator,  appears  to  be  connected  with 
that  of  the  changes  in  the  earth's  magnetism.  They  are  of 
daily  occurrence,  but  feeble  except  whenever  there  is  a  dis- 
play of  aurora,  and  during  a  magnetic  storm ;  but  it  is  not 
yet  determined  whether  these  currents  are  due  to  the  varia- 
tions in  the  magnetism  of  the  earth,  or  whether  those  varia- 
tions are  due  to  the  currents.  It  is  believed  that  the  evapo- 
ration (see  Art.  72)  always  going  on  in  the  tropics  causes  the 
ascending  currents  of  heated  air  to  be  electrified  positively 
relatively  to  the  earth.  Probably  the  ionizing  action  (Art. 
632)  of  ultra-violet  light  in  the  upper  regions  has  also  some 
share.  The  air-currents  travel  northward  and  southward 
toward  the  colder  polar  regions,  where  they  descend.  These 
streams  of  electrified  air  will  act  (see  Art.  429)  like  true  elec- 
tric currents,  and  as  the  earth  rotates  within  them  it  will  be 
acted  upon  magnetically.  The  author  has  for  many  years 
upheld  the  view  that  this  thermodynamic  production  of 
polar  currents  in  conjunction  with  the  earth's  diurnal  rota- 
tion affords  the  only  rational  means  yet  suggested  for 
accounting  for  the  growth  of  the  earth's  magnetism  to  its 
present  state.  The  action  of  the  sun  and  moon  in  raising 
tides  in  the  atmosphere  might  account  for  the  variations 
mentioned  in  Art.  162.  It  is  important  to  note  that  in  all 
magnetic  storms  the  intensit}'  of  the  perturbations  is  greatest 
in  the  regions  nearest  the  poles ;  also,  that  the  magnetic 
poles  coincide  very  nearly  with  the  regions  of  greatest  cold ; 
that  the  region  where  aurorae  (Art.  361)  are  seen  in  greatest 
abundance  is  a  region  lying  nearly  symmetrically  round  the 
magnetic  pole. 


CHAPTER  III 

CURRENT   ELECTRICITY 

LESSON  XIII.  —  Simple  Voltaic  Cells 

169.  Flow  of  Currents.  —  It  has  been  already  mentioned, 
in  Lesson  IV.,  how  electricity  flows  away  from  a  charged 
body  through  any  conducting  substance,  such  as  a  wire  or  a 
wetted  string.  If,  by  any  arrangement,  electricity  could  be 
supplied  to  the  body  just  as  fast  as  it  flowed  away,  a  con- 
tinuous current  would  be  produced.  Such  a  current  always 
flows  through  a  conducting  wire,  if  the  ends  are  kept  at 
different  electric  potentials.  In  like  manner,  a  current  of 
heat  flows  through  a  rod  of  metal  if  the  ends  are  kept  at 
different  temperatures,  the  flow  being  always  from  the  high 
temperature  to  the  lower.  It  is  convenient  to  regard  the 
electricity  as  flowing  from  positive  to  negative.  The 
natural  direction  of  an  electric  current  is  from  the  high  poten- 
tial to  the  low ;  such  a  flow  tends  to  equalize  the  potential. 
In  order  that  a  continuous  flow  may  be  kept  up  there  must 
be  a  circuit l — that  is,  a  conducting  path  —  provided.  The 
" current"  has  sometimes  been  regarded  as  a  double  transfer, 
of  positive  electricity  in  one  direction  and  of  negative  elec- 
tricity in  the  opposite  direction.  The  only  evidence  to  sup- 
port this  very  unnecessary  supposition  is  the  fact  that,  in 
the  decomposition  of  liquids  by  the  current,  some  of  the 
elements  are  liberated  at  the  place  where  the  current  enters, 
others  at  the  place  where  it  leaves  the  liquid.  Another 

1  The  conductors  connected  with  a  source  of  electrical  supply  are  col- 
lectively called  the  "circuit."  When  they  form  a  closed  path  through 
which  a  current  circulates  there  is  a  "closed  circuit."  When  the  path  is 
not  closed  and  no  current  circulates  there  is  an  "open  circuit." 

144 


CH.  m.  170,171]        GALVANI   AND   VOLTA  145 

notion  is  that  the  "  current  "  consists  in  swarms  of  electrons 
(or  negative  particles)  flowing  along  the  circuit  from  negative 
to  positive.  No  final  evidence  exists  as  to  the  direction  in 
which  the  current  in  a  wire  really  "  flows." 

The  quantity  of  electricity  conveyed  by  a  current  is  pro- 
portional to  the  current  and  to  the  time  that  it  continues  to 
flow.  The  practical  unit  of  current  is  called  the  ampere 
(see  Arts.  220  and  381).  The  quantity  of  electricity  con- 
veyed by  a  current  of  one  ampere  in  one  second  is  called  one 
ampere-second  or  one  coulomb.  One  ampere-hour  equals  3600 
coulombs.  If  i  is  the  number  of  amperes  of  current,  t  the 
number  of  seconds  that  it  lasts,  and  Q  the  number  of  coulombs 
of  electricity  thereby  conveyed,  the  relation  between  them 
is  expressed  by  the  formula  :  — 

Q  =  i  X  t. 

Example.  —  If  a  current  of  80  amperes  flows  for  15  minutes 
the  total  quantity  of  electricity  conveyed  will  be 
80  X  15  X  60  =  72,000  coulombs.  This  is  equal  to  20 
ampere-hours. 

170.  Continuous    and    Alternating    Currents.  —  Currents 
are  called  continuous  if  they  flow,  without  stopping,  in  one 
direction.     They  are  called  alternating  currents  if  they  con- 
tinually reverse  in  direction,  in  a  regular  periodic  manner, 
flowing  first  in  one  direction  round  the  circuit  and  then  in 
the  other. 

Continuous  currents  of  electricity  are  produced  by  voltaic 
cells,  and  batteries  of  such  cells,  or  else  by  dynamos  driven  by 
power,  though  there  are  other  sources  of  currents  hereafter 
to  be  mentioned.  Alternating  currents  are  produced  by 
special  alternating  current  dynamos  or  alternators,  and  are 
separately  treated  of  in  Art.  534  (p.  515). 

171.  Discoveries   of   Galvani   and   of   Volta.  —  The   dis- 
covery of  electric  currents  originated  with  Galvani,  a  phy- 
sician of  Bologna,  who,  about  the  year  1786,  made  a  series 
of  curious  and  important  observations  upon  the  convulsive 
motions  produced  by  the  "  return-shock  "    (Art.    29)    and 


146  ELECTRICITY   AND  MAGNETISM       [PT.  i.  172 

other  electric  discharges  upon  a  frog's  leg.  He  was  led  by 
this  to  the  discovery  that  it  was  not  necessary  to  use  an 
electric  machine  to  produce  these  effects,  but  that  a  similar 
convulsive  kick  was  produced  in  the  frog's  leg  when  two  dis- 
similar metals,  iron  and  copper,  for  example,  were  placed  in 
contact  with  a  nerve  and  a  muscle  respectively,  and  then 
brought  into  contact  with  each  other.  Galvani  imagined 
this  action  to  be  due  to  electricity  generated  by  the  frog's 
leg  itself.  It  was,  however,  proved  by  Volta,  Professor  in 
the  University  of  Pavia,  that  the  electricity  arose  not  from 
the  muscle  or  nerve,  but  from  the  contact  of  the  dissimilar 
metals.  When  two  metals  are  placed  in  contact 
with  one  another  in  the  air,  one  becomes  posi- 
tive and  the  other  negative,  though  the  charges 
are  very  feeble.  Volta,  however,  proved  their 
reality  by  two  different  methods. 

172.  The  Voltaic  Pile.  —  The  second  of 
Volta's  proofs  consisted  in  showing  that  when 
a  number  of  such  contacts  of  dissimilar  metals 
could  be  arranged  so  as  to  add  their  electrical 
effects  together,  those  effects  were  more  power- 
ful in  proportion  to  the  number  of  the  contacts. 
FlG'  10piI^V°lta's  witn  this  view  he  constructed, the  apparatus 
known  (in  honour  of  the  discoverer)  as  the 
Voltaic  Pile  (Fig.  104).  It  is  made  by  placing  a  pair  of 
disks  of  zinc  and  copper  in  contact  with  one  another,  then 
laying  on  the  copper  disk  a  piece  of  flannel  or  blotting-paper 
moistened  with  brine,  then  another  pair  of  disks  of  zinc  and 
copper,  and  so  on,  each  pair  of  disks  in  the  pile  being  sepa- 
rated by  a  moist  conductor.  Such  a  pile,  if  composed  of  a 
number  of  such  pairs  of  disks,  will  produce  electricity  enough 
to  give  quite  a  perceptible  shock,  if  the  top  and  bottom 
disks,  or  wires  connected  with  them,  be  touched  simul- 
taneously with  the  moist  fingers.  When  a  single  pair  of 
metals  are  placed  in  contact,  one  becomes  +  ly  electrical  to 
a  certain  small  extent,  and  the  other  — ly  electrical,  or,  in 


CH.  in.  173,  174] 


VOLTAIC   CELL 


147 


other  words,  there  is  a  certain  difference  of  electric  potential 
(see  Art.  283)  between  them.  But  when  a  number  are  thus 
set  in  series  with  moist  conductors  between  the  successive 
pairs,  the  difference  of  potential  between  the  first  zinc  and 
the  last  copper  disk  is  increased  in  proportion  to  the  num- 
ber of  pairs ;  for  now  all  the  successive  small  differences  of 
potential  are  added  together. 

173.  The  Crown  of  Cups.  —  Another  combination  devised 
by  Volta  was  his  Couronne  de  -Tasses  or  Crown  of  Cups.  It 
consisted  of  a  number  of  cups  (Fig.  105),  filled  either  with 


FIG.  105.  —  Crown  of  Cups. 

brine  or  dilute  acid,  into  which  dipped  a  number  of  com- 
pound strips,  half  zinc  half  copper,  the  zinc  portion  of  one 
strip  dipping  into  one  cup,  while  the  copper  portion  dipped 
into  the  other  cup.  The  difference  of  potential  between 
the  first  and  last  cups  is  again  proportional  to  the  number 
of  pairs  of  metal  strips.  This  arrangement,  though  badly 
adapted  for  such  a  purpose,  is  powerful  enough  to  ring  an 
electric  bell,  the  wires  of  which  are  joined  to  the  first  zinc 
and  the  last  copper  strip.  The  electrical  action  of  these 
combinations  is,  however,  best  understood  by  studying  the 
phenomena  of  one  single  cup  or  cell. 

174.  Simple  Voltaic  Cell.  —  Place  in  a  glass  jar  some 
water  having  a  little  sulphuric  acid  or  any  other  oxidizing 
acid  added  to  it  (Fig.  106).  Place  in  it  separately  two 
clean  strips,  one  of  zinc  Z,  and  one  of  copper  C.  This  cell 
is  capable  of  supplying  a  continuous  flow  of  electricity 


148 


ELECTRICITY   AND   MAGNETISM       [PT.  i.  174 


r 


through  a  wire  whose  ends  are  brought  into  connexion  with 
the  two  strips.  When  the  current  flows  the  zinc  strip  is 
observed  to  waste  away ;  its  consumption  in  fact  furnishes  the 

energy  required  to  drive  the 
current  through  the  cell  and 
the  connecting  wire.  The 
cell  may  therefore  be  re- 
garded as  a  sort  of  chemical 
furnace  in  which  fuel  is  con- 
sumed to  drive  the  current. 
The  zinc  is  the  fuel,1  the  acid 
is  the  aliment,  whilst  the 
copper  is  merely  a  metallic 
hand  let  down  into  the  cell 
to  pick  up  the  current,  and 
takes  no  part  chemically. 
So  long  as  no  metallic  con- 
tact is  made  with  either  of 
the  metals  no  appreciable  difference  of  potential  between 
the  copper  and  the  zinc  will  be  observable,  even  by  using 
a  delicate  electrometer,  because  the  electrometer  merely 
measures  the  potential  at  a  point  in  the  air  or  oxidizing 
medium  outside  the  zinc  or  the  copper,  not  the  poten- 
tials of  the  metals  themselves.  The  zinc  is  trying  to 
dissolve  and  send  a  current  across  to  the  copper;  while 
the  copper  is  trying  (less  powerfully)  to  dissolve  and  drive 
a  current  across  the  other  way.  The  zinc  itself  is  at 
about  1-83  volts  higher  potential  than  the  surrounding 
oxidizing  media  (see  Art.  568) ;  while  the  copper  is  at  only 
about  0-80  volts  higher,  having  a  less  tendency  to  become 
oxidized.  There  is  then  a  latent  difference  of  potential  of 
about  1  -03  volts  between  the  zinc  and  the  copper ;  but  this 
produces  no  current  as  long  as  there  is  no  metallic  circuit. 
If  the  strips  are  made  to  touch,  or  are  joined  by  a  pair  of 


FIG.  106.  —  Voltaic  Cell. 


1  Zinc,  as  is  well  known,  will  burn  with  a  blue  flame  in  air  or  oxygen, 
giving  out  heat.     Zinc  foil  is  easily  kindled. 


CH.  in.  174]  CURRENT   EFFECTS  149 

metal  wires,  immediately  there  is  a  rush  of  electricity  through 
the  acid  from  the  zinc  to  the  copper,  as  indicated  by  the 
arrows  in  Fig.  106,  the  current  returning  by  the  metal  cir- 
cuit from  the  copper  to  the  zinc.  A  small  portion  of  the  zinc 
is  at  the  same  time  dissolved  away ;  the  zinc  parting  with  its 
latent  energy  as  its  atoms  combine  with  the  acid.  This 
energy  is  expended  in  forcing  electricity  through  the  acid 
to  the  copper  strip,  and  thence  through  the  wire  circuit 
back  to  the  zinc  strip.  The  copper  strip,  whence  the  cur- 
rent starts  on  its  journey  through  the  external  circuit,  is 
called  the  positive  pole,  and  the  zinc  strip  is  called  the  nega- 
tive pole.  If  two  copper  wires  are  united  to  the  tops  of  the 
two  strips,  though  no  current  flows  so  long  as  the  wires  are 
kept  separate,  the  wire  attached  to  the  zinc  will  be  found 
to  be  negative,  and  that  attached  to  the  copper  positive, 
there  being  still  a  tendency  for  the  zinc  to  oxidize  and  drive 
electricity  through  the  cell  from  zinc  to  copper.  This  state 
of  things  is  represented  by  the  +  and  -  signs  in  Fig.  106  ; 
and  this  distribution  of  potentials  led  some  to  consider  the 
junction  of  the  zinc  with  the  copper  wire  as  the  starting  point 
of  the  current.  But  the  real  starting  point  is  in  the  cell  at 
the  surface  of  the  zinc  where  the  chemical  action  is  furnish- 
ing energy  ;  for  from  this  point  there  are  propagated  through 
the  liquid  certain  electro-chemical  actions  (more  fully  ex- 
plained in  Chap.  XIII.)  which  have  the  result  of  constantly 
renewing  the  difference  of  potential.  At  the  same  time  it 
will  be  noticed  that  a  few  bubbles  of  hydrogen  gas  appear 
on  the  surface  of  the  copper  plate.  Both  these  actions  go 
on  as  long  as  the  wires  are  joined  to  form  a  complete  circuit. 
The  metallic  zinc  may  be  considered  as  a  store  of  energy. 
We  know  that  if  burned  as  a  fuel  in  oxygen  or  air  it  will  ' 
give  out  that  store  of  energy  as  heat.  If  burned  in  this 
quiet  chemical  manner  in  a  cell  it  gives  out  its  store  not  as 
heat  —  any  heat  in  a  cell  is  so  much  waste  —  but  in  the  form 
of  electric  energy,  i.e.  the  energy  of  an  electric  current  pro- 
pelled by  an  electromotive  force. 


150  ELECTRICITY   AND   MAGNETISM    [PT.  i.  175,  176 

175.  Effects  produced  by  Current.  —  The  current  itself 
cannot  be  seen  to  flow  through  the  wire  circuit;    hence  to 
prove  that  any  particular  cell  or  combination  produces  a 
current  requires  a  knowledge  of  some  of  the  effects  which 
currents  can  produce.     These  are  of  various  kinds,     (i.)  A 
current  flowing  through  a  thin  wire  will  heat  it ;    (ii.)   flow- 
ing near  a  magnetic  needle  it  will  cause  it  to  turn  aside,  or 
circulating  in  a  coil  around  a  rod  of  iron  will  magnetize  it ; 
(iii.)  flowing  through  water  and  other  liquids  it  decomposes 
them;    (iv.)  and,  lastly,  flowing  through  the  living  body  or 
any  sensitive  portion  of  it,  it  produces  certain  sensations. 
These  effects,  thermal,  magnetic,  chemical,  and  physiological, 
will  be  considered  in  special  lessons. 

176.  Voltaic  Battery.  —  If  a  number  of  such  simple  cells 
are  united  in  series,  the  zinc  plate  of  one  joined  to  the  copper 
plate  of  the  next,  and  so  on,  a  greater  difference  of  poten- 
tials will  be  produced  between  the 

HI]  ill]  I copper  "  pole  "  at  one  end  of  the 
II     I       ~    series  and  the  zinc  "pole"  at  the 

no.  107. -Cells  in  Series.  °ther    6ncL       HenC6>    Wnen    the    tW° 

poles  are  joined  by  a  wire  there  will 

be  a  more  powerful  flow  of  electricity  than  one  cell  would 
cause.  Such  a  combination  of  Voltaic  Cells  is  called  a  Vol- 
taic Battery.1  There  are  many  ways  of  grouping  a  battery 
of  cells,  but  two  need  special  notice.  If  the  cells  are  joined 
up  in  one  row,  as  in  Fig.  105  or  Fig.  107,  they  are  said  to  be 
in  series.  Electricians  often  represent  a  cell  by  a  symbol  in 
which  a  short  thick  line  stands  for  the  zinc  and  a  longer  thin 
line  for  the  copper  (or  carbon).  Thus  Fig.  107  represents 

1  By  some  writers  the  name  Galvanic  Battery  is  given  in  honour  of  Galvani ; 
but  the  honour  is  certainly  Volta's.  The  electricity  that  flows  thus  in 
currents  is  sometimes  called  Voltaic  Electricity,  or  Galvanic  Electricity,  or 
sometimes  even  Galvanism  ( !) ,  but,  as  we  shall  see,  it  differs  only  in  degree 
from  Frictional  or  any  other  Electricity,  and  both  can  flow  along  wires,  and 
magnetize  iron,  and  decompose  chemical  compounds.  The  word  Battery 
means  an  arrangement  of  two  or  more  cells ;  just  as  in  warfare  a  -battery  of 
guns  mean  an  arrangement  of  two  or  more  guns. 


CH.  in.  177]  ELECTROMOTIVE-FORCE  151 

four  cells  joined  in  series.  So  joined  they  cannot  yield  more 
current  (more  amperes)  than  a  single  cell  would  yield,  but 
they  yield  that  current  with  a  fourfold  electromotive-force 
(i.e.  with  more  volts  of  pressure). 

The  other  chief  way  of  grouping  cells  is  to  join  all  the  zincs 
together  and  all  the  coppers  (or  carbons)  together ;  and  they 
are  then  said  to  be  in  parallel,  or  _ 

are  joined    "  for   quantity."      So 
joined  they  have  no  greater  electro- 
motive-force than   one  cell.     The 
zincs  act  like  one  big  zinc,   the       FlQ.  108.  -  ceils  in  Parallel, 
coppers  like  one  big  copper.     But 

they  will  yield  more  current.  Fig.  108  shows  the  four  cells 
grouped  in  parallel;  they  would  yield  thus  a  current  four 
times  as  great  as  one  cell  alone  would  yield. 

177.  Electromotive-Force.  —  The  term  electromotive-force 
is  employed  to  denote  that  which  moves  or  tends  to  move 
electricity  from  one  place  to  another.1  For  brevity  we  some- 
times write  it  E.M.F.  In  this  particular  case  it  is  obviously 
the  result  of  the  difference  of  potential,  and  proportional  to 
it.  Just  as  in  water-pipes  a  difference  of  level  produces  a 
pressure,  and  the  pressure  produces  a  flow  so  soon  as  the 
tap  is  turned  on,  so  difference  of  potential  produces  electro- 
motive-force, and  electromotive-force  sets  up  a  current  so 
soon  as  a  circuit  is  completed  for  the  electricity  to  flow 
through.  Electromotive-force,  therefore,  may  often  be 
conveniently  expressed  as  a  difference  of  potential,  and 
vice  versa;  but  the  student  must  not  forget  the  distinction. 
The  unit  in  which  electromotive-force  is  measured  is  termed 


1  The  beginner  must  not  confuse  Electromotive-force,  or  that  which  tends 
to  move  electricity,  with  Electric  ''force,1'  or  that  force  with  which  elec- 
tricity tends  to  move  charged  matter.  Newton  has  virtually  defined 
"force,"  once  for  all,  as  that  which  moves  or  tends  to  move  matter.  When 
matter  is  moved  by  a  magnet  we  speak  rightly  of  magnetic  force;  when 
electricity  moves  matter  we  may  speak  of  electric  force.  But  E.M.F.  is 
quite  a  different  thing,  not  "force"  at  all,  for  it  acts  on  electricity,  and  tends 
to  make  it  move  round  the  circuit. 


152  ELECTRICITY   AND   MAGNETISM      [PT.  i.  178 

the  volt  (see  Art.  381).  The  terms  pressure  and  voltage  are 
sometimes  used  for  difference  of  potential  or  electromotive- 
force. 

178.  Volta's  Laws.  —  Volta  showed  (Art.  80)  that  the 
difference  of  potential  between  two  metals  in  contact  (in 
air)  depended  merely  on  what  metals  they  were,  not  on  their 
size,  nor  on  the  amount  of  surface  in  contact.  He  also 
showed  that  when  a  number  of  metals  touched  one  another 
the  difference  of  potential  between  the  first  and  last  of  the 
row  is  the  same  as  if  they  touched  one  another  directly. 
A  quantitative  illustration  from  the  researches  of  Ayrton 
and  Perry  was  given  in  Art.  81.  But  the  case  of  a  series 
of  cells  is  different  from  that  of  a  mere  row  of  metals  in 
contact.  If  in  the  row  of  cells  the  zincs  and  coppers  are  all 
arranged  in  one  order,  so  that  all  of  them  set  up  electromo- 
tive-forces in  the  same  direction,  the  total  electromotive-force 
of  the  series  will  be  equal  to  the  electromotive-force  of  one  cell 
multiplied  by  the  number  of  cells. 

Hitherto  we  have  spoken  only  of  zinc  and  copper  as  the 
materials  for  a  cell ;  but  cells  may  be  made  of  any  two  metals. 
The  effective  electromotive-force  of  a  cell  depends  on  the 
difference  between  the  two.  If  zinc  were  used  for  both 
plates  in  a  cell  it  would  give  no  current,  for  each  plate  would 
be  trying  to  dissolve  and  to  drive  a  current  across  to  the 
other  with  equal  tendency.  That  cell  will  have  the  greatest 
electromotive-force,  or  be  the  most  "  intense,"  in  which 
those  materials  are  used  which  have  the  greatest  difference 
in  their  tendency  to  combine  chemically  with  the  acid,  or 
which  are  widest  apart  on  the  "  contact-series  "  given  in 
Art.  81  (p.  77).  Zinc  and  copper  are  convenient  in  this 
respect ;  and  zinc  and  silver  would  be  better  but  for  the 
expense.  For  more  powerful  batteries  a  zinc-platinum  or  a 
zinc-carbon  combination  is  preferable.  That  plate  or  piece 
of  metal  in  a  cell  by  which  the  current  enters  the  liquid  is 
called  the  anode;  it  is  that  plate  which  dissolves  away. 
The  plate  or  piece  of  metal  by  which  the  current  leaves  the 


CH.  in.  179]  RESISTANCE  153 

cell  is  called  the  kathode;  it  is  not  dissolved,  and  in  some 
cases  receives  a  deposit  on  its  surface. 

179.  Resistance.  —  The  same  electromotive-force  does 
not,  however,  always  produce  a  current  of  the  same  strength. 
The  amount  of  current  depends  not  only  on  the  electro- 
motive-force tending  to  drive  the  electricity  round  the 
circuit,  but  also  on  the  resistance  (see  Art.  432)  which  it 
has  to  encounter  and  overcome  in  its  flow.  If  the  cells  be 
partly  choked  with  sand  or  sawdust  (as  is  sometimes  done 
in  so-called  "  Sawdust  Batteries  "  to  prevent  spilling),  or, 
if  the  wire  provided  to  complete  the  circuit  be  very  long 
or  very  thin,  the  action  will  be  partly  stopped,  and  the 
current  will  be  weaker,  although  the  E.M.F.  may  be  un- 
changed. The  analogy  of  the  water-pipes  will  again  help 
us.  The  pressure  which  forces  the  water  through  pipes 
depends  upon  the  difference  of  level  between  the  cistern 
from  which  the  water  flows  and  the  tap  to  which  it  flows ; 
but  the  amount  of  water  that  runs  through  will  depend  not 
on  the  pressure  alone,  but  on  the  resistance  it  meets  with ; 
for,  if  the  pipe  be  of  very  small  bore,  or  choked  with  sand 
or  sawdust,  very  little  water  will  run  through. 

Metals  in  general  conduct  well :  their  resistance  is  small. 
The  longer  wires  are,  and  the  thinner  they  are  the  more  will 
they  resist ;  thus  permitting  a  smaller  current  to  flow  through 
the  circuit.  The  liquids  in  the  cell  do  not  conduct  nearly 
so  well  as  the  metals,  and  different  liquids  have  different 
resistances.  Pure  water  will  hardly  conduct  at  all,  and  is 
for  the  feeble  electromotive-force  of  the  voltaic  battery 
almost  a  perfect  insulator;  though  for  the  high-potential 
electricity  of  the  frictional  machines  it  is,  as  we  have  seen, 
a  fair  conductor.  Salt  and  sal-ammoniac  dissolved  in  water 
are  good  conductors,  and  so  are  dilute  acids,  though  strong 
sulphuric  acid  is  a  bad  conductor.  The  resistance  of  the 
liquid  in  the  cells  may  be  reduced,  if  desired,  by  using  larger 
plates  of  metal  and  putting  them  nearer  together.  Gases 
are  bad  conductors ;  hence  the  films  of  hydrogen  gas  which 


154  ELECTRICITY   AND   MAGNETISM       [PT.  i.  180 

are  given  off  at  the  copper  plate  during  the  action  of  the 
cell,  and  which  stick  to  the  surface  of  the  copper  plate, 
increase  the  internal  resistance  of  the  cell  by  diminishing  the 
effective  surface  of  the  plates.  Some  of  the  rare  earths  are 
found  to  be  good  conductors  when  hot.  Such  an  earthy 
oxide  is  used  in  the  Nernst  lamp  (Art.  485) . 

LESSON  XIV.  —  Chemical  Actions  in  the  Cell 

180.  Chemical  Actions.  —  The  production  of  a  current 
of  electricity  by  a  voltaic  cell  is  always  accompanied  by 
chemical  actions  in  the  cell.  One  of  the  metals  at  least 
must  be  readily  oxidizable,  and  the  liquid  must  be  one 
capable  of  acting  on  the  metal.  Zinc  and  the  other  metals 
which  stand  at  the  electropositive  end  of  the  contact-series 
(see  Art.  81)  are  oxidizable;  whilst  the  electronegative 
substances  —  copper,  silver,  gold,  platinum,  and  graphite 
—  are  less  oxidizable,  and  the  last  three  resist  the  action 
of  every  single  acid.  There  is  no  proof  that  their  electrical 
behaviour  is  due  to  their  chemical  properties ;  nor  that  their 
chemical  behaviour  is  due  to  their  electrical  properties. 
Probably  both  result  from  a  common  cause  (see  Art.  81, 
and  also  Art.  568).  A  piece  of  quite  pure  zinc  when  dipped 
alone  into  dilute  pure  sulphuric  acid  is  not  attacked  by  the 
liquid.  But  the  ordinary  commercial  zinc  is  not  pure,  and 
when  plunged  into  dilute  sulphuric  acid  dissolves  away,  a 
large  quantity  of  bubbles  of  hydrogen  gas  being  given  off 
from  the  surface  of  the  metal.  Sulphuric  acid  is  a  complex 
substance,  in  which  every  molecule  is  made  up  of  a  group  of 
atoms  —  2  of  Hydrogen,  1  of  Sulphur,  and  4  of  Oxygen ; 
or,  in  Symbols,  H2SO4.  The  chemical  reaction  by  which 
the  zinc  enters  into  combination  with  the  radical  of  the 
acid,  turning  out  the  hydrogen,  is  expressed  in  the  following 
equation :  — 

Zn      +          H2SO4  ZnS04          +          H2 

Zinc     and     Sulphuric  Acid    produce  Sulphate  of  Zinc    and     Hydrogen 


CH.  in.  181]  CHEMICAL  ACTIONS  155 

The  sulphate  of  zinc  produced  in  this  reaction  remains  in 
solution  in  the  liquid. 

When  a  plate  of  pure  zinc  and  a  plate  of  some  less  easily 
oxidizable  metal  —  copper  or  platinum,  or,  best  of  all, 
carbon  (the  hard  carbon  from  gas  retorts)  —  are  put 
side  by  side  into  the  cell  containing  acid,  no  appreciable 
chemical  action  takes  place  until  the  circuit  is  completed 
by  joining  the  two  plates  with  a  wire,  or  by  making  them 
touch  one  another.  Directly  the  circuit  is  completed  a 
current  flows  and  the  chemical  actions  begin,  the  zinc  dis- 
solving in  the  acid,  and  the  acid  giving  up  its  hydrogen  in 
streams  of  bubbles.  But  these  bubbles  of  hydrogen  are 
evolved  not  at  the  zinc  plate,  nor  yet  throughout  the  liquid, 
but  at  the  surface  of  the  copper  plate  (or  the  carbon  plate  if 
carbon  is  employed) .  This  invisible  transfer  of  the  hydrogen 
gas  through  the  liquid  from  the  surface  of  the  zinc  plate  to 
the  surface  of  the  copper  plate  where  it  appears  is  very  re- 
markable. The  ingenious  theory  framed  by  Grotthuss  to 
account  for  it  is  explained  in  Art.  570  (p.  558). 

These  chemical  actions  go  on  as  long  as  the  current  passes. 
The  quantity  of  zinc  used  up  in  each  cell  is  proportional 
to  the  amount  of  electricity  which  flows  round  the  circuit 
while  the  battery  is  at  work ;  or,  in  other  words,  is  propor- 
tional to  the  current.  The  quantity  of  hydrogen  gas 
evolved  is  also  proportional  to  the  amount  of  zinc  consumed, 
and  also  to  the  current.  After  the  acid  has  thus  dissolved 
zinc  in  it,  it  will  no  longer  act  as  a  corrosive  solvent;  it  has 
been  "  killed,"  as  workmen  say,  for  it  has  been  turned  into 
sulphate  of  zinc.  The  battery  will  cease  to  act,  therefore, 
either  when  the  zinc  has  all  dissolved  away,  or  when  the 
acid  has  become  exhausted,  that  is  to  say,  when  it  is  all 
turned  into  sulphate  of  zinc.  Stout  zinc  plates  will  last  a 
long  time,  but  the  acids  require  to  be  renewed  frequently, 
the  spent  liquor  being  emptied  out. 

181.  Local  Action.  —  When  the  circuit  is  not  closed  the 
current  cannot  flow,  and  there  should  be  no  chemical  action 


156  ELECTRICITY  AND   MAGNETISM       [PT.  i.  182 

so  long  as  the  battery  is  producing  no  current,  The  impure 
zinc  of  commerce  does  not  remain  quiescent  in  the  acid, 
but  is  continually  dissolving  and  giving  off  hydrogen  bubbles. 
This  local  action,  as  it  is  termed,  is  explained  in  the  following 
manner  :  —  The  impurities  in  the  zinc  consist  of  particles  of 
iron,  arsenic,  and  other  metals.  Suppose  a  particle  of  iron 
to  be  on  the  surface  anywhere  and  in  contact  with  the  acid. 
It  will  behave  like  the  copper  plate  of  a  battery  towards 
the  zinc  particles  in  its  neighbourhood,  for  a  local  difference 
of  potential  will  be  set  up  at  the  point  where  there  is  metallic 
contact,  causing  a  local  or  parasitic  current  to  run  from  the 
particles  of  zinc  through  the  acid  to  the  particle  of  iron,  and  so 
there  will  be  a  continual  wasting  of  the  zinc,  both  when  the 
battery  circuit  is  closed  and  when  it  is  open. 

182.  Amalgamation  of  Zinc.  —  We  see  now  why  a  piece 
of  ordinary  commerical  zinc  is  attacked  on  being  placed  in 
acid.  There  is  local  action  set  up  all  over  its  surface  in 
consequence  of  the  metallic  impurities  in  it.  To  do  away 
with  this  local  action,  and  abolish  the  wasting  of  the  zinc 
while  the  battery  is  at  rest,  it  is  usual  to  amalgamate  the 
surface  of  the  zinc  plates  with  mercury.  The  surface  to  be 
amalgamated  should  be  cleaned  by  dipping  into  acid,  and 
then  a  few  drops  of  mercury  should  be  poured  over  the  surface 
and  rubbed  into  it  with  a  bit  of  linen  rag  tied  to  a  stick.  The 
mercury  unites  with  the  zinc  at  the  surface,  forming  a  pasty 
amalgam.  The  iron  particles  do  not  dissolve  in  the  mercury, 
but  float  up  to  the  surface,  whence  the  hydrogen  bubbles 
which  may  form  speedily  carry  them  off.  As  the  zinc  in 
this  pasty  amalgam  dissolves  into  the  acid  the  film  of  mer- 
cury unites  with  fresh  portions  of  zinc,  and  so  presents 
always  a  clean  bright  surface  to  the  liquid. 

A  newer  and  better  process  is  to  add  about  4  per  cent  of 
mercury  to  the  molten  zinc  before  casting  into  plates  or 
rods.  If  the  zinc  plates  of  a  battery  are  well  amalgamated 
there  should  be  no  evolution  of  hydrogen  bubbles  when  the 
circuit  is  open.  Nevertheless  there  is  still  always  a  little 


CH.  in.  183, 184]    POLARIZATION   IN   CELLS  157 

wasteful  local  action  during  the  action  of  the  battery.  Jacobi 
found  that  while  one  part  of  hydrogen  was  evolved  at  the 
kathode,  33 '6  parts  of  zinc  were  dissolved  at  the  anode, 
instead  of  the  32 '5  parts  which  are  chemically  the  equivalent 
of  the  hydrogen. 

183.  Polarization.  —  The     molecules     of     hydrogen     gas 
liberated  at  the  surface  of  the  copper  plate  stick  to  it  in 
great  numbers,   and  form  a  film  over  its  surface ;    hence 
the  effective  amount  of  surface  of  the  copper  plate  is  very 
seriously  reduced  in  a  short  time.     When   a  simple  cell, 
or  battery  of  such  cells,  is  set  to  produce  a  current,  it  is 
found  that  the  current  after  a  few  minutes,  or  even  seconds, 
falls  off  very  greatly,  and  may  even  be  almost  stopped.     This 
immediate  falling  off  in  the  current,  which  can  be  observed 
with  any  galvanometer  and  a  pair  of  zinc  and  copper  plates 
dipping  into  acid,  is  almost  entirely  due  to  the  film  of  hydro- 
gen gas  sticking  to  the  surface  of  the  copper  pole.     A  battery 
which  is  in  this  condition  is  said  to  be  "  polarized." 

184.  Effects    of    Polarization.  —  The    film    of    hydrogen 
bubbles  affects  the  strength  of  the  current  of  the  cell  in 
two  ways. 

Firstj  it  weakens  the  current  by  the  increased  resist- 
ance which  it  offers  to  the  flow,  for  films  of  gas  are  bad 
conductors ;  and,  worse  than  this, 

Second,  it  weakens  the  current  by  setting  up  an  opposing 
electromotive-force;  for  hydrogen  is  almost  as  oxidizable  a 
substance  as  zinc,  especially  when  it  is  being  deposited 
(or  in  a  "  nascent  "  state),  and  is  electropositive,  standing 
between  lead  and  iron  in  the  series  on  p.  78.  Hence  the 
hydrogen  itself  produces  a  difference  of  potential,  which 
would  tend  to  start  a  current  in  the  opposite  direction  to  the 
true  zinc-to-copper  current.  No  cell  in  which  the  polariza- 
tion causes  a  rapid  falling  off  in  power  can  be  used  for  con- 
tinuous working.  It  is  therefore  a  very  important  matter 
to  abolish  this  polarization,  otherwise  the  current  furnished 
by  batteries  does  not  remain  constant. 


158          ELECTRICITY   AND   MAGNETISM     [PT.  i.  185,  186 

185.  Remedies   against   Internal    Polarization.  —  Various 
remedies   have   been   practised   to   reduce   or   prevent   the 
polarization  of  cells.     These  may  be  classed  as  mechanical, 
chemical,  and  electrochemical. 

1.  Mechanical    Means.  —  If    the    hydrogen    bubbles    be 
simply   brushed   away   from   the   surface   of   the   kathode, 
the  resistance  they  caused  will  be  diminished.     If  air  be 
blown  into  the  acid  solution  through  a  tube,  or  if  the  liquid 
be  agitated  or  kept  in  constant  circulation  by  siphons,  the 
resistance  is  also  diminished.     If  the  surface  be  rough  or 
covered  with  points,  the  bubbles  collect  more  freely  at  the 
points  and  are  quickly  carried  up  to  the  surface,  and  so 
got  rid  of.     This  remedy  was  applied  in  Smee's  Cell,  which 
consisted  of  a  zinc  and  a  platinized  silver  plate  dipping  into 
dilute  sulphuric  acid;    the  silver  plate,  having  its  surface 
thus  covered  with  a  rough  coating  of  finely  divided  platinum, 
gave  up  the  hydrogen  bubbles  freely ;    nevertheless,  in  a 
battery  of  Smee  Cells  the  current  diminishes  greatly  after 
a  few  minutes. 

2.  Chemical    Means.  —  If    a    highly-oxidizing    substance 
be  added  to  the  acid  it  will  destroy  the  hydrogen  bubbles 
whilst  they  are  still   in  the  nascent   state,   and  thus  will 
prevent  both  the  increased  internal  resistance  and  the  oppos- 
ing electromotive-force.     Such  substances  are  bichromate  of 
potash,  nitric  acid,  chlorine  and  the  peroxides. 

3.  Electrochemical  Means.  —  It  is  possible  by  employing 
double  cells,  as  explained  in  the  next  lesson,  to  so  arrange 
matters  that  some  solid  metal,  such  as  copper,  shall  be  liber- 
ated instead  of  hydrogen  bubbles,  at  the  point  where  the 
current  leaves  the  liquid.     This  electrochemical    exchange 
entirely  obviates  polarization. 

186.  Simple  Laws  of  Chemical  Action  in  the  Cell.  —  We 
will  conclude  this  section  by  enumerating  the  two  simple 
laws  of  chemical  action  in  the  cell. 

I.    The  amount  of  chemical  action  in  the  cell  is  proportional 
to  the  quantity  of  electricity  that  passes  through  it  — •  that  is 


CH.  in.  1ST]  VOLTAIC   CELLS  159 

to  say,  is  proportional  to  the  current  while  it  passes,  and  to 
the  time  during  which  it  is  passing. 

A  current  of  one  ampere  flowing  through  the  cell  for  one 
second  causes  0  00033873  (or  2-9^2)  °f  a  gramme  of  zinc  to 
dissolve  in  the  acid,  and  liberates  0'00001044  (or  g-sr-gr)  of  a 
gramme  of  hydrogen. 

II.  In  a  battery  consisting  of  cells  joined  in  series,  the 
amounts  of  chemical  action  are  equal  in  each  cell. 

The  first  of  these  laws  was  thought  by  Faraday,  who 
discovered  it,  to  disprove  Volta's  contact  theory.  He 
foresaw  that  the  principle  of  the  conservation  of  energy 
would  preclude  a  mere  contact  force  from  furnishing  a 
continuous  supply  of  current,  and  hence  ascribed  the  cur- 
rent to  the  chemical  actions  which  were  proportional  in 
quantity  to  it.  How  the  views  of  Volta  and  Faraday  are 
to  be  harmonized  has  been  indicated  in  the  last  paragraph 
of  Art.  81.  These  laws  relate  only  to  the  useful  chemical 
action,  and  do  not  include  the  waste  by  "  local  "  actions 
(Art.  181)  due  to  parasitic  currents  set  up  by  impurities. 

LESSON  XV.  —  Voltaic  Cells 

187.  A  good  Voltaic  cell  should  fulfil  all  or  most  of  the 
following  conditions :  — 

1.  Its    electromotive-force    should    be    high    and    con- 

stant. 

2.  Its  internal  resistance  should  be  small. 

3.  It  should  give   a   constant   current,   and  therefore 

must  be  free  from  polarization,  and  not  liable 
to  rapid  exhaustion,  requiring  frequent  renewal 
of  the  acid. 

4.  It  should  be  perfectly  quiescent  when  the  circuit 

is  open. 

5.  It  should  be  cheap  and  of  durable  materials. 

6.  It  should  be  manageable,  and,  if  possible,  should 

not  emit  corrosive  fumes. 


160  ELECTRICITY  AND   MAGNETISM          [PT.  i.  188 

No  single  cell  fulfils  all  these  conditions,  however,  and 
some  cells  are  better  for  one  purpose  and  some  for  another. 
Thus,  for  telegraphing  through  a  long  line  of  wire  a  con- 
siderable internal  resistance  in  the  battery  is  no  great  dis- 
advantage; while,  for  producing  an  electric  arc,  much 
internal  resistance  is  absolutely  fatal.  The  electromotive- 
force  of  a  battery  depends  on  the  materials  of  the  cell,  and 
on  the  number  of  cells  linked  together;  a  high  E.M.F.  can 
therefore  be  gained  by  choosing  the  right  substances  and  by 
taking  a  large  number  of  cells.  The  resistance  within  the 
cell  can  be  diminished  by  increasing  the  size  of  the  plates, 
by  bringing  them  near  together,  so  that  the  thickness  of  the 
liquid  between  them  may  be  as  small  as  possible,  and  by 
choosing  liquids  that  are  good  conductors.  Cells  are  some- 
times classified  into  two  groups,  according  as  they  contain 
one  or  two  fluids,  or  electrolytes,  but  a  better  classification 
is  that  adopted  in  Art.  185,  depending  on  the  means  of  pre- 
venting polarization. 

188.   Cells  of  Class  I. — WITH  MECHANICAL  DEPOLAKIZATION 

The  simple  cell  of  Volta,  with  its  zinc  and  copper  plates, 
has  been  already  described.  The  larger  the  copper  plate, 
the  longer  the  time  which  it  takes  to  polarize.  Cruickshank 
suggested  to  place  the  plates  vertically  in  a  trough,  producing 
a  more  powerful  combination.  Dr.  Wollaston  proposed  to 
use  a  plate  of  copper  of  double  size,  bent  round  so  as  to 
approach  the  zinc  on  both  sides,  thus  diminishing  the  resist- 
ance, and  allowing  the  hydrogen  more  surface  to  deposit 
upon.  Smee,  as  we  have  seen,  replaced  the  copper  plate  by 
platinized  silver,  and  Walker  suggested  the  use  of  plates  of 
hard  carbon  instead  of  copper  or  silver,  thereby  saving  cost, 
and  at  the  same  time  increasing  the  electromotive-force. 
The  roughness  of  the  surface  facilitates  the  escape  of  hydro- 
gen bubbles.  By  agitating  such  cells,  or  raising  their  kathode 
plates  for  a  few  moments  into  the  air,  their  power  is  partially 


CH.  in.  189]     EXCITANTS  AND   DEPOLARIZERS 


161 


restored.  The  Law  cell,  used  in  the  United  States  for  open- 
circuit  work,  is  of  this  class :  it  has  a  small  rod  of  zinc  and 
a  cleft  cylinder  of  carbon  of  large  surface  immersed  in  a 
solution  of  sal-ammoniac. 


189.   Cells  of  Class  II.  —  WITH  CHEMICAL  DEPOLARIZATION 

In  these  cells,  in  addition  to  the  dilute  acid  or  other 
excitant  to  dissolve  the  zinc,  there  is  added  some  more 
powerful  chemical  agent  as  a  depolarizer.  Amongst  de- 
polarizers the  following  are  used :  —  Nitric  acid,  solutions 
of  chromic  acid,  bichromate  of  potash,  bichromate  of  soda, 
nitrate  of  potash,  or  ferric  chloride ;  chlorine ;  black  oxide 
of  manganese,  sulphur,  per- 
oxide of  lead,  red  lead,  oxide 
of  copper.  Most  of  these 
materials  would,  however,  at- 
tack the  copper  as  well  as  the 
zinc  if  used  in  a  zinc-copper 
cell.  Hence  they  can  only 
be  made  use  of  in  zinc-carbon 
or  zinc-platinum  cells.  Nitric 
acid  also  attacks  zinc  when 
the  circuit  is  open.  Hence  it 
cannot  be  employed  in  the 
same  single  cell  with  the 
zinc  plate.  In  the  Bichromate 
Cell,  invented  by  Poggendorff, 
bichromate  of  potash  is  added 

to  the  sulphuric  acid.  This  cell  is  most  conveniently  made 
up  as  shown  in  Fig.  109,  in  which  a  plate  of  zinc  is  the  anode, 
and  a  pair  of  carbon  plates,  one  on  each  side  of  the  zinc, 
joined  together  at  the  top  serve  as  a  kathode.  As  this 
solution  would  attack  the  zinc  even  when  the  circuit  is  open, 
the  zinc  plate  is  fixed  to  a  rod  by  which  it  can  be  drawn 
up  out  of  the  solution  when  the  cell  is  not  being  worked. 

M 


FIG.  109.  —  Bichromate  Cell. 


162  ELECTRICITY  AND   MAGNETISM        [PT.  i.  190 

To  obviate  the  necessity  of  this  operation  the  device  is 
adopted  of  separating  the  depolarizer  from  the  excitant 
liquid  into  which  the  zinc  dips.  In  the  case  of  liquid  de- 
polarizers this  is  done  by  the  use  of  an  internal  porous  cell 
or  partition.  Porous  cells  of  earthenware  or  of  parchment 
paper  allow  the  electric  current  to  flow  while  keeping  the 
liquids  apart.  In  one  compartment  is  the  zinc  anode 
dipping  into  its  aliment  of  dilute  acid ;  in  the  other  com- 
partment the  carbon  (or  platinum)  kathode  dipping  into 
the  depolarizer.  Such  cells  are  termed  two-fluid  cells.  In  the 
case  of  solid  depolarizers  such  as  black  oxide  of  manganese, 
oxide  of  copper,  etc.,  the  material  merely  needs  to  be  held 
up  to  the  kathode.  All  solid  depolarizers  are  slow  in  acting. 

190.  Grove's  Cell.  —  Sir  William  Grove  devised  a  cell 
in  which  there  is  an  outer  cell  of  glazed  ware  or  of  ebonite, 
containing  the  amalgamated  zinc  plate  and  dilute  sulphuric 
acid.  In  the  inner  porous  cell  a  piece  of  platinum  foil  serves 
as  the  kathode,  and  it  dips  into  the x  strongest  nitric  acid. 
There  is  no  polarization  in  this  cell,  for  the  hydrogen  ions 
liberated  by  the  solution  of  the  zinc  in  dilute  sulphuric  acid, 
in  passing  through  the  nitric  acfd  in  order  to  appear  at  the 
platinum  pole,  decompose  the  nitric  acid  and  are  oxidized, 
producing  water  and  the  red  fumes  of  nitric  peroxide  gas. 
This  gas  does  not,  however,  produce  polarization,  for  as  it  is 
very  soluble,  it  does  not  form  a  film  upon  the  face  of  the 
platinum  plate,  nor  does  it,  like  hydrogen,  set  up  an  opposing 
electromotive-force  with  the  zinc.  Grove  cells  may  be  made 
of  a  flat  shape,  the  zinc  being  bent  up  so  as  to  embrace  the 
flat  porous  cell  on  both  sides.  This  reduces  the  internal 
resistance,  which  is  already  small  on  account  of  the  good 
conducting  powers  of  nitric  acid.  A  Grove's  cell  will  furnish 
for  three  or  four  hours  continuously  a  current  of  12  to  15 
amperes.  The  E.M.F.  of  one  cell  is  about  1*9  volts,  and  its 
internal  resistance  is  very  low  (about  O'l  ohm  for  the  quart 
size).  A  single  cell  will  readily  raise  to  a  bright  red  heat 
two  or  three  inches  of  thin  platinum  wire.  Years  ago,  to 


CH.  III.   191] 


BUNSEN'S   CELL 


163 


produce  an  arc  light,  it  was  usual  to  employ  a  battery  of  fifty 
Grove's  cells  joined  in  series,  the  platinum  of  one  cell  being 
clamped  to  the  zinc  of  the  cell  next  to  it. 

191.  Bunsen's  Cell.  —  The  cell  which  bears  Bunsen's  name 
is  a  modification  of  that  of  Grove.  In  the  Bunsen  cell  the 
expensive l  platinum  foil  is  replaced  by  a 
rod  or  slab  of  hard  gas  carbon.  A  cylin- 
drical form  of  cell,  with  a  rod  of  carbon,  is 
shown  in  Fig.  110.  The  voltage  for  a 
zinc-carbon  combination  is  a  little  higher 
than  for  a  zinc-platinum  one,  which  is  an 
advantage ;  but  the  Bunsen  cell  is  trouble- 
some to  keep  in  order,  and  there  is  some 
difficulty  in  making  a  good  contact  be- 
tween the  rough  surface  of  the  carbon 
and  the  copper  strap  which  connects  the 
carbon  of  one  cell  to  the  zinc  of  the 
next.  The  top  part  of  the  carbon  is  sometimes  impregnated 
with  paraffin  wax  to  keep  the  acid  from  creeping  up,  and 


FIG.  110.—  Bunsen  Cell. 


FIG.  111.  —  Battery  of  five  Bunsen  Cells  in  Series. 

electro  typed  with  copper.     Fig.  Ill  shows  the  usual  way  of 
coupling  up  a  series  of  five  such  cells.     Bunsen's  battery  will 

1  Platinum  costs  about  240  shillings  an  ounce  —  nearly  thrice  as  much  as 
gold ;  while  a  hundredweight  of  the  gas  carbon  may  be  had  for  a  mere  trifle, 
often  for  nothing  more  than  the  cost  of  carrying  it  from  the  gasworks.  An 
artificial  carbon  prepared  by  grinding  up  gas  carbon  with  some  carbonaceous 
matter  such  as  tar,  sugar  residues,  etc.,  then  pressing  into  moulds,  and 
baking  in  a  furnace,  is  used  both  for  battery  plates  and  for  the  carbon  rods 
used  in  arc  lamps. 


164 


ELECTRICITY  AND   MAGNETISM        [PT.  i.  192 


continue  to  furnish  a  current  for  a  longer  time  than  the  flat 
Grove's  cells,  on  account  of  the  larger  quantity  of  acid 
contained  by  the  cylindrical  pots.1 

Chromic  solutions,  formed  by  adding  strong  sulphuric 
acid  to  solutions  of  bichromate  of  potash  or  of  soda,  are 
often  used  instead  of  nitric  acid,  in  cells  of  this  form.  Soluble 
depolarizers  in  the  form  of  chromic  powders  are  made  by 
heating  strong  sulphuric  acid  and  gradually  stirring  into  it 
powdered  bichromate  of  soda.  The  pasty  mass  is  then 
cooled  and  powdered. 

192.  Leclanche' s  Cell.  —  For  working  electric  bells  and 
telephones,  and  also  to  a  limited  extent  in  telegraphy,  a 
zinc-carbon  cell  invented  by  Leclanche  is  employed,  in  which 

the  exciting  liquid 
c  is  not  dilute  acid, 
but  a  solution  of 
sal-ammoniac.  In 
this  the  zinc  dis- 
solves, forming  a 
double  chloride  of 
zinc  and  ammonia, 
while  ammonia  gas 
and  hydrogen  are 

liberated  at  the  carbon  pole.  The  depolarizer  is  the  black 
dioxide  of  manganese,  fragments  of  which,  mixed  with 
powdered  carbon,  are  held  up  to  the  carbon  kathode  either 
by  packing  them  together  inside  a  porous  pot  or  by  being 
attached  as  an  agglomerated  block.  The  oxide  of  man- 
ganese will  slowly  yield  up  oxygen  as  required.  If  used 
to  give  a  continuous  current  for  many  minutes  together, 
the  power  of  this  cell  falls  off  owing  to  the  accumulation 
of  the  hydrogen  bubbles;  but  if  left  to  itself  for  a  time 

1  Callan  constructed  a  large  battery  in  which  cast  iron  formed  the  positive 
pole,  being  immersed  in  strong  nitric  acid,  the  zincs  dipping  into  dilute  acid. 
The  iron  under  these  circumstances  is  not  acted  upon  by  the  acid,  but 
assumes  a  so-called  "passive  "  state.  In  this  condition  its  surface  appears  to 
be  impregnated  with  a  film  of  magnetic  peroxide,  or  of  oxygen. 


FIG.  112.  —  Battery  of  three  Leclanche  Cells  in  Series. 


CH.  in.  193-195]  LALANDE'S   CELL  165 

the  cell  recovers  itself,  the  dioxide  gradually  destroying  the 
polarization.  As  the  cell  is  in  other  respects  perfectly 
constant,  and  does  not  require  renewing  for  months  or  years, 
it  is  well  adapted  for  domestic  purposes.  It  has  the  advan- 
tage of  not  containing  corrosive  acids.  Millions  of  these  cells 
are  in  use  on  "  open-circuit  "  service  —  that  is  to  say,  for 
those  cases  in  which  the  current  is  only  required  for  a  few 
moments  at  a  time,  and  the  circuit  usually  left  open.  Three 
Leclanche  cells  are  shown  joined  in  series,  in  Fig.  112.  Com- 
mon salt  may  be  used  instead  of  sal-ammoniac. 

193.  Dry   Cells.  —  This  name  is  given  to    modifications 
of  the  Leclanche  cell  in  which  the  excitant  cannot  be  spilled. 
The  space  between  the  zinc,  which  forms  the  case,  and  the 
interior   depolarizing   mass   is   filled   up   with   a   porous   or 
gelatinous  paste  of  sawdust,  paper-pulp,  or  flour,  often  mixed 
with  plaster  of  Paris,  and  impregnated  with  a  solution  of 
sal-ammoniac,  with  a  little  chloride  of  zinc  to  keep  the  mass 
moist,  then  covered  with  a  layer  of  pitch  or  bitumen.     The 
chemical  action  is  the  same  as  in  the  Leclanche  cell,  and  the 
voltage  is  about  1*4  volts,  slowly  falling  as  the  cell  is  used. 

194.  Lalande's   Cell.  —  The  anode  is  zinc,   and   the  ex- 
citing liquid  is  a  30  per  cent  solution  of  caustic  potash  into 
which  the  zinc  dissolves  (forming  zincate  of  potash),  whilst 
the  kathode  consists  of  a  compressed  cake  of  the  red  oxide 
of   copper   which   becomes   gradually   reduced   to   metallic 
copper.     It  is  mechanically  held  to  a  frame  of  copper  or 
iron.     The  cell  has  only  0'8  to  0'9  volts  of  E.M.F.,  but  is 
capable  of  yielding  a  large  and  constant  current. 

195.    Cells  of  Class  III.  —  WITH   ELECTROCHEMICAL   DE- 
POLARIZATION 

When  any  soluble  metal  is  immersed  in  a  solution  of  its 
own  salt  —  for  example,  zinc  dipped  into  sulphate  of  zinc, 
or  copper  into  sulphate  of  copper  —  there  is  a  definite 
electromotive-force  between  it  and  its  solution,  the  measure 


166 


ELECTRICITY   AND   MAGNETISM       [PT.  i.  196 


of  its  tendency  to  dissolve.  If  a  current  is  sent  from  metal 
to  solution  some  of  the  metal  dissolves;  if,  however,  the 
current  is  sent  from  solution  to  metal  some  more  metal  will 
be  deposited  (or  "  plated  ")  out  of  the  solution.  But  as 
long  as  the  chemical  nature  of  the  surface  and  of  the  liquid 
is  unchanged  there  will  be  no  change  in  the  electromotive- 
force  at  the  surface.  It  follows  that  if  a  cell  were  made 
with  two  metals,  each  dipping  into  a  solution  of  its  own  salt, 
the  two  solutions  being  kept  apart  by  a  porous  partition, 
such  a  cell  would  never  change  its  electromotive-force.  The 
anode  would  not  polarize  where  it  dissolves  into  the  excitant ; 
the  kathode  would  not  polarize,  since  it  receives  merely  an 
additional  thickness  of  the  same  sort  as  itself.  This  elec- 
trochemical method  of  avoiding  polarization  was  discovered 
by  Daniell.  It  is  the  principle  not  only  of  the  Daniell  cell, 
but  of  the  Clark  cell  and  of  others.  For  perfect  constancy 
the  two  salts  used  should  be  salts  of  the  same  acid,  both 
sulphates,  or  both  chlorides,  for  example. 

196.    Daniell' s  Cell.  —  An  element  of  a  DanielFs  battery 
(Fig.  113)  consists  of  an  outer  cell,  usually  of  copper,  which 
serves  as  kathode,  and  an  inner  cylin- 
drical cell  of  unglazed  porous  ware  (a 
cell   of  parchment,  or   even   of   brown 
paper,    will    answer),    within   which    is 
placed  a  rod  of  amalgamated  zinc  as 
anode.     The  liquid  in  the  inner  cell  is 
dilute  sulphuric  acid  or  dilute  sulphate 
of   zinc ;    that   in   the   outer   cell   is   a 
saturated  solution  of  sulphate  of  copper 
FIG.  113.  —  Danieii's  Cell.    ("  blue  vitriol"),  some  spare  crystals  of 
the  same  substance  being  contained  in  a 
perforated  shelf  at  the  top  of  the  cell,  in  order  that  they  may 
dissolve  and  replace  that  which  is  used  up  while  the  battery 
is  in  action. 

When  the  circuit  is  closed  the  zinc  dissolves  in  the  dilute 
acid,   forming  sulphate  of  zinc,   and  liberating  hydrogen; 


CH.  in.  196]  DANIELL'S   CELL  167 

but  this  gas  does  not  appear  in  bubbles  on  the  surface  of  the 
copper  cell,  for,  since  the  inner  cell  is  porous,  the  molecular 
actions  (by  which  the  freed  atoms  of  hydrogen  are,  as  ex- 
plained by  Fig.  336,  handed  on  through  the  acid)  traverse 
the  pores  of  the  inner  cell,  and  there,  in  the  solution  of 
sulphate  of  copper,  the  hydrogen  atoms  are  exchanged  for 
copper  atoms,  the  result  being  that  pure  copper,  and  not 
hydrogen  gas,  is  deposited  on  the  outer  common  plate. 
Chemically  these  actions  may  be  represented  as  taking 
place  in  two  stages. 

Zn         +          H2S04  ZnS04       +        H2 

Zinc         and      Sulphuric  Acid      produce  Sulphate  of  Zinc  and  Hydrogen 

And  then 

H2       +         CuSO4  H2SO4       +      Cu. 

Hydrogen  and  Sulphate  of  Copper  produce  Sulphuric  Acid  and  Copper. 

The  hydrogen  is,  as  it  were,  translated  electrochemically 
into  copper  during  the  round  of  changes,  and  so  while  the 
zinc  dissolves  away  the  copper  grows,  the  dilute  sulphuric 
acid  gradually  changing  into  sulphate  of  zinc,  and  the  sul- 
phate of  copper  into  sulphuric  acid.  In  the  case  in  which  a 
solution  of  sulphate  of  zinc  is  used  there  is  no  need  to  consider 
any  hydrogen  atoms,  copper  being  exchanged  chemically 
for  zinc.  There  is  therefore  no  polarization  so  long  as  the 
copper  solution  is  saturated ;  and  the  cell  is  very  constant, 
thought  not  so  constant  in  all  cases  as  Clark's  standard  cell 
described  in  Art.  200,  owing  to  slight  variations  in  the 
electromotive-force  as  the  composition  of  the  other  fluid 
varies.  When  sulphuric  acid  diluted  with  twelve  parts  of 
water  is  used  the  E.M.F.  is  1-178  volts.  The  E.M.F.  is 
1-07  volts  when  concentrated  zinc  sulphate  is  used;  1-1 
volts  when  a  half-concentrated  solution  of  zinc  sulphate  is 
used ;  and,  in  the  common  cells  made  up  with  water  or 
dilute  acid,  1-1  volts  or  less.  Owing  to  its  constancy,  this 
battery,  made  up  in  a  convenient  flat  form  (Fig.  116),  has 
been  much  used  in  telegraphy.  It  is  indispensable  in  those 


168  ELECTRICITY  AND   MAGNETISM   [PT.  i.  197-200 

"  closed  circuit  "  methods  of  telegraphy  (Art.  583),  where 
the  current  is  kept  always  flowing  until  interrupted  by 
signalling.  The  function  of  the  porous  partition  is  to  keep 
the  two  fluids  from  mixing ;  for  the  solution  of  sulphate  of 
copper  must  not  be  allowed  to  come  into  contact  with  the 
zinc,  otherwise  there  would  be  deleterious  local  action. 

197.  De    la    Rue's    Battery.  —  De- la    Rue    constructed 
a  constant  cell  belonging  to  Class  III.,  in  which  zinc  and 
silver  are  the  two  metals,  the  zinc  being  immersed  in  chloride 
of  zinc,  and  the  silver  embedded  in  a  stick  of  fused  chloride 
of   silver.     As  the  zinc  dissolves   away,  metallic   silver   is 
deposited  upon  the  kathode,  just  as  the  copper  is  in  the 
DanielPs  cell.     De  la  Rue  constructed  an  enormous  battery 
of  over  1 1,000  little  cells.     The  difference  of  potential  between 
the  first  zinc  and  last  silver  of  this  battery  was  over  11,000 
volts. 

198.  Gravity    Cells.  —  Instead    of    employing    a    porous 
cell  to  keep  the  two  liquids  separate,  it  is  possible,  where 
one  of  the  liquids  is  heavier  than  the  other,  to  arrange  that 
the  heavier  liquid  shall  form  a  stratum  at  the  bottom  of 
the  cell,  the  lighter  floating  upon  it.     Such  arrangements 
are  called  gravity  cells ;   but  the  separation  is  never  perfect, 
the  heavy  liquid  slowly  diffusing  upwards.     Daniell's  cells 
arranged  as  gravity  cells  have  been  contrived  by  Meidinger, 
Minotto,  Callaud,  and  Lord  Kelvin. 

199.  Effect  of  Heat  on  Cells.  —  If  a  cell  be  warmed  it 
yields  a  stronger  current  than  when  cold.     This  is  chiefly 
due  to  the  fact  that  the  liquids  conduct  better  when  warm, 
the  internal  resistance  being  thereby  reduced.     A  change 
is  also  observed  in  the  E.M.F.  on  heating ;  thus  the  E.M.F. 
of  a  Daniell's  cell  is  about  1J  per  cent  higher  when  warmed 
to  the  temperature  of  boiling  water,  while  that   of   a  bi- 
chromate battery  falls  off  nearly  2  per  cent  under  similar 
circumstances. 

200.  Standard    Cells.  —  For    purposes    of    standardiza- 
tion and  testing  a  cell  is  required  the  E.M.F.  of  which  is 


CH.  in.  201] 


STANDARD   CELLS 


169 


_G/ass  tube 


-Cork 

Air-bubble 
Zinc  sulphate 
-  Crystals 

Paste 
Mercury 


Platinum  wire 
FIG.  114.  —  Clark  Standard  Cell. 


constant  and  independent  of  all  local  conditions.  A  form 
of  Daniell's  cell  designed  by  Fleming  answers  this  purpose 
for  ordinary  use.  A  standard  cell  whose  E.M.F.  is  even 
more  constant  than  that  of  the 
Daniell  was  suggested  by  Latimer 
Clark.  The  Clark  Cell,  which  was 
at  one  time  adopted  as  the  inter- 
national standard,  consists  of  an 
anode  of  pure  zinc  in  a  concen- 
trated solution  of  zinc-sulphate, 
whilst  the  kathode  is  of  pure 
mercury  in  contact  with  a  paste 
of  mercurous  sulphate.  Fig.  114 
shows,  in  actual  size,  the  form 
of  the  Clark  cell.  Its  E.M.F.  is 
1434  volts  at  14°  C.,  but  it  drops  slightly  if  the  tempera- 
ture rises.  Its  E.M.F.,  at  any  temperature  of  0°  C.,  may  be 
calculated  by  the  formula 

E.M.F.  =  [1434  (1-0-00077(0°  -  14)]  volt. 

Lord  Rayleigh  suggested  a  modification  known  as  the 
"  H-form,"  in  which  the  materials  are  contained  in  a  glass 
vessel  in  the  form  of  the  letter  H.  Zinc  amalgam  is  con- 
tained in  one  limb,  and  the  mercury  and  mercurous  sul- 
phate in  the  other ;  the  whole  being  filled  with  a  saturated 
zinc  sulphate  solution.  One  electrode  is  introduced  through 
the  bottom  of  each  limb.  This  type  of  cell  has  the  advantage 
that  the  position  of  the  electrodes  is  definitely  fixed  so  that 
there  is  no  liability  to  local  action.  Von  Helmholtz  proposed 
to  substitute  mercurous  chloride  (calomel)  and  zinc  chloride, 
in  place  of  sulphates,  but  the  combination  has  no  advantages. 

201.  The  Weston  Normal  Cell.  —  This  cell  resembles  the 
Clark,  save  in  having  cadmium  instead  of  zinc.  Fig.  115 
shows  it  as  made  up  in  the  H-pattern.  One  limb  contains 
cadmium  amalgam,  the  other  mercury  covered  with  a  paste 
of  mercurous  sulphate.  The  whole  is  filled  with  a  solu- 


170 


ELECTRICITY   AND   MAGNETISM       [PT.  i.  202 


tion  of  cadmium  sulphate  kept 
saturated  by  inserting  in  each 
limb  some  crystals  of  cadmium 
sulphate  which  crust  together 
and  form  as  it  were  plugs 
below  the  constrictions  of  the 
tubes.  Its  E.M.F.  is  1-0183 
volts  at  20°  C.  The  voltage 
falls  by  0-00004  for  a  tempera- 

FIG.  115.  -Weston  Normal  Cell.  tui>6     rise      °f      One     Centigrade 

degree. 

Within  the  range  0°  to  40°  C.,  the  E.M.F.  at  tempera- 
ture t°  C.,  is:  — 


Et  =  E20  -  0-0000406(*  -  20)  -  J9-5  X 


-  20)2j. 


202.  Other  Cells.  —  Numerous  other  forms  of  battery 
have  been  suggested  by  different  electricians.  There  are 
three,  of  theoretical  interest  only,  in  which,  instead  of 
using  two  metals  in  one  liquid  which  attacks  them  unequally, 
two  liquids  are  used  having  unequal  chemical  action  on  the 
metal.  In  these  there  is  no  contact  of  dissimilar  metals. 
The  first  of  these  was  invented  by  Napoleon  III.  Both 
plates  were  of  copper  dipping  respectively  into  solutions  of 
dilute  sulphuric  acid  and  of  cyanide  of  potassium,  separated 
by  a  porous  cell.  The  second  of  these  combinations,  due 
to  Wholer,  employs  plates  of  aluminium  only,  dipping  respec- 
tively into  strong  nitric  acid  and  a  solution  of  caustic  soda. 
In  the  third,  invented  by  Dr.  Fleming,  the  two  liquids  do 
not  even  touch  one  another,  being  joined  together  by  a  second 
metal.  In  this  case  the  liquids  chosen  are  sodium  per- 
sulphide  and  nitric  acid,  and  the  two  metals  copper  and 
lead.  A  similar  battery  might  be  made  with  copper  and 
zinc,  using  solutions  of  ordinary  sodium  sulphide  and  of 
dilute  sulphuric  acid  in  alternate  cells,  a  bent  zinc  plate 
dipping  into  the  first  and  second  cells,  a  bent  copper  plate 
dipping  into  second  and  third,  and  so  on;  for  the  electro- 


CH.  in.  203,  204]      MISCELLANEOUS   CELLS  171 

motive-force  of  a  copper  sodium-sulphide  zinc  combina- 
tion is  in  the  reverse  direction  to  that  of  a  copper  sulphuric- 
acid  zinc  combination. 

The  Fitch  cell,  used  in  the  United  States,  is  a  zinc-carbon 
cell  with  an  excitant  composed  of  salammonaic  solution 
to  which  the  chlorates  of  potash  and  soda  have  been  added 
to  depolarize. 

Jablochkoff  described  a  batter^in  which  plates  of  carbon 
and  iron  are  placed  in  fused  nitre ;  the  carbon  is  here  the 
electropositive  element,  being  rapidly  consumed  in  the  liquid. 

Planters  and  Faure's  Secondary  Batteries,  and  Grove's 
Gas  Battery,  are  described  in  Arts.  572,  574. 

203.  Zamboni's    Dry    Pile.  —  The    so-called    Dry    Pile 
of  Zamboni  consists  of  a  number  of  paper  disks,   coated 
with  zinc-foil  on  the  side  and  with  dioxide  of  manganese 
on  the  other,  piled  up  on  one  another,  to  the  number  of 
some  thousands,  in  a  glass  tube.      Its   internal  resistance 
is  enormous,  as  the  internal  conductor  is  the  moisture  of 
the  paper,  and  this  is  slight ;    but  its  electromotive-force 
is  very  great,  and  a  good  dry  pile  will  yield  sparks.     Many 
years  may  elapse  before  the  zinc  is  completely  oxidized 
or  the  manganese  exhausted.     In  the  Clarendon  Laboratory 
at  Oxford  there  is  a  dry  pile,  the  poles  of  which  are  two  metal 
bells :   between  them  is  hung  a  small  brass  ball,  which,  by 
oscillating  to  and  fro,  slowly  discharges  the  electrification. 
It  has  now  been  continuously  ringing  the  bells  since  the  year 
1842. 

204.  Statistics   of   Cells.  —  The   table   on  the  following 
page  gives  the  electromotive-forces  of  the  various  batteries 
enumerated. 

The  E.M.F.  of  the  single-fluid  cells  of  Volt  a  and  Smee  is 
marked  in  the  table  as  doubtful,  for  the  opposing  E.M.F. 
of  polarization  sets  in  almost  before  the  true  E.M.F.  of  the 
cell  can  be  measured.  The  different  values  assigned  to  other 
cells  are  accounted  for  by  the  different  degrees  of  concentra- 
tion of  the  liquids.  Thus  in  the  Daniell's  cells  used  in 


172 


ELECTRICITY   AND   MAGNETISM       [PT.  i.  205 


telegraphy,  water  only  is  supplied  at  first  in  the  cells  con- 
taining the  zincs ;  and  the  E.M.F.  of  these  is  less  than  if 
acid  or  sulphate  of  zinc  were  added  to  the  water. 


NAME 

ANODE 

EXCITANT 

DEPOLAR- 
IZER 

KATHODE 

APPROXIMATE 
VOLTS 

(Solution 

Class  I. 

of) 

Volta  (Wollaston, 

Zinc 

H2SO4 

none 

Copper 

I'O  to  '05 

etc.)  

Smee       .... 

Zinc 

H2SO4 

none 

Platinized 

I'D  to  0'5 

• 

silver 

Law  

Zinc 

NH4CL 

none 

Carbon 

I'O  to  0'5 

Class  II. 

Poggendorff  (Gre- 

Zinc 

H2SO4 

K2Cr2O 

Carbon 

2'0 

net,  Fuller,  etc.). 

Grove     .... 

Zinc 

H2SO4 

HNOs 

Platinum 

T9 

Bunsen  .... 

Zinc 

H2S04 

HN03 

Carbon 

T9 

Leclanch6   .     .     . 

Zinc 

NH4C1 

MnO2 

Carbon 

1'4 

Lalande       .     .     . 

Zinc 

KHO 

CuO 

Carbon 

0-8 

Fitch      .... 

Zinc 

NH4C1 

KC103 

Carbon 

I'l 

NaClO3 

Class  III. 

Daniell  (  Meidinger, 

Zinc 

ZnSO4 

CuS04 

Copper 

1-07 

Minotto,  etc.). 

De  la  Rue  .     .     . 

Zinc 

ZnCl2 

AgCl 

Silver 

1'42 

Marie  Davy    .     . 

Zinc 

ZnSO4 

Hg6S04 

Carbon 

1-4 

Von  Helmholtz     . 

Zinc 

ZnCl2 

Hg2Cl2 

Mercury 

I'O 

Clark   (Standard) 

Zinc 

ZnSO4 

Hg2S04 

Mercury 

1-434 

Weston  (Standard) 

Cadmium 

CdS04 

Hg2SO4 

Mercury 

1-0183 

Class  IV. 

Accumulators. 

(Plante,Faure,etc.) 

Lead 

H2S04 

PbO2 

Lead 

2-1  to  1-85 

Edison    .... 

Iron 

KHO 

NiO 

Steel 

1-35  to  1-25 

205.  Strength  of  Current.  —  The  definition  of  the  strength 
of  a  current  is  as  follows :  The  strength  of  a  current  is  the 
quantity  of  electricity  which  flows  past  any  point  of  the  circuit 
in  one  second.1  Suppose  that  at  the  end  of  10  seconds  25 
coulombs  of  electricity  have  passed  through  a  circuit,  then 
the  average  current  during  that  time  has  been  2J  coulombs 
per  second,  or  2J  amperes.  The  usual  currents  employed  in 

:The  phrases  "strength  of  current,"  "intensity  of  current,"  "quantity 
of  current,"  are  old-fashioned,  and  mean  no  more  than  "current"  means 
—  that  is  to  say,  the  number  of  amperes  that  are  flowing. 


CH.  in.  206] 


CURRENT   STRENGTH 


173 


telegraphing  over  main  lines  are  only  from  five  to  ten  thou- 
sandths of  an  ampere. 

If  in  t  seconds  a  quantity  of  electricity  Q  has  flowed 
through  the  circuit,  then  the  average  current  i  during  that 
time  is  represented  by  the  equation 

•     Q 

l=t 

This  should  be  compared  with  Art.  169. 

The  student  must  remember  that  the  strength  of  current 
which  the  various  batteries  will  yield  depends  (Art.  179)  on 
the  internal  resistance  of  the  cells  and  on  that  of  their  circuit, 
as  well  as  on  their  E.M.F.  The  E.M.F.  of  a  cell  is  indepen- 
dent of  its  size,  and  is  determined  solely  by  the  materials 
chosen  and  their  condition.  The  resistance  depends  on  the 
size  of  the  cell,  the  conducting  qualities  of  the  liquid,  the 
thickness  of  the  liquid  which  the  current  must  traverse,  etc. 

The  internal  resistances  of  cells  vary  greatly.  The 
maximum  current  which  a  cell  will  give  on  short-circuit 
through  a  stout  wire,  or  when  short-circuited  by  an  ampere- 
meter, can  be  found  by  dividing  the  E.M.F.  by  the  internal 
resistance,  as  in  the  following  cases  :  — 


NAME 

E.M.F. 

(volts) 

INTERNAL  RESIST- 
ANCE (ohms) 
(Approximately) 

CURRENT  ON  SHORT- 
CIRCUIT 
(amperes) 

Bichromate    . 

2-0 

0'2 

10 

Grove    1 
Bunsen  J 

1'9 

0'15 

12.6 

Leclanche  .     . 

1-4 

0'5 

2.8 

Lalande     .     . 

0'8 

O'l 

8.0 

Gassner  (dry) 
Daniell      .     . 

1*4 

1'07 

0'2 

ro 

7.0 
1.07 

206.  Ohm's  Law.  —  The  laws  which  determine  the 
strength  or  quantity  of  a  current  in  a  circuit  were  first 
enunciated  by  Dr.  G.  S.  Ohm,  who  stated  them  in  the 
following  law :  —  The  current  varies  directly  as  the  electro- 


174  ELECTRICITY   AND   MAGNETISM        [PT.  i.  207 

motive-force,  and  inversely  as  the  resistance  of  the  circuit; 
or,  in  other  words,  anything  that  makes  the  E.M.F.  of  the 
cell  greater  will  increase  the  current,  while  anything  that 
increases  the  resistance  (either  the  internal  resistance  in  the 
cells  themselves  or  the  resistance  of  the  external  wires  of 
the  circuit)  will  diminish  the  current. 
In  symbols  this  becomes 

E 

R=*' 

where  E  is  the  number  of  volts,  R  the  number  of  ohms  of 
the  circuit,  and  i  the  number  of  amperes  of  current. 

Example.  —  To  find  the  current  that  can  be  sent  through  a 
resistance  of  5  ohms  by  an  E.M.F.  of  20  volts.  20  -^  5  =  4 
amperes. 

(See  further  concerning  Ohm's  Law  in  Lesson  XXXIII, 
p.  400.)  Ohm's  Law  says  nothing  about  the  energy  or 
power  conveyed  by  a  current.  The  power  of  a  current 
is  proportional  both  to  the  current  and  to  the  electromotive- 
force  which  drives  it  (see  Art.  454). 

207.  Resistance  and  Grouping  of  Cells.  —  The  internal 
resistances  of  the  cells  we  have  named  differ  very  greatly, 
and  differ  with  their  size.  Broadly  speaking,  we  may  say 
that  the  resistance  in  a  Daniell's  cell  is  about  five  times  that 
in  a  Grove's  cell  of  equal  size.  The  Grove's  cell  has  indeed 
both  a  higher  E.M.F.  and  less  internal  resistance.  It  would 
in  fact  send  a  current  about  eight  times  as  strong  as  the 
Daniell's  cell  of  equal  size  through  a  short  stout  wire  of 
negligible  resistance.  The  Lalande  cell  has  a  remarkably 
small  internal  resistance. 

We  may  then  increase  the  strength  of  a  battery  in  two 
ways : 

(1)  By  increasing  its  E.M.F. 

(2)  By  diminishing  its  internal  resistance. 

The  electromotive-force  of  a  cell  being  determined  by 
the  materials  of  which  it  is  made,  the  only  way  to  increase 
the  total  E.M.F.  of  a  battery  of  given  materials  is  to  in- 


CH.  in.  207]  GROUPING   OF   CELLS  175 

crease  the  number  of  cells  joined  "  in  series."  It  is  frequent 
in  the  telegraph  service  to  link  thus  together  two  or  three 
hundred  of  the  flat  Daniell's  cells;  and  they  are  usually 


FIG.  116.  —  Battery  of  Ten  Daniell  Cells  in  Series. 

made  up  in  trough-like  boxes,  containing  a  series  of  10  cells, 
as  shown  in  Fig.  116. 

To  diminish  the  internal  resistance  of  a  cell  the  following 
expedients  may  be  resorted  to  : 

(1)  The  plates  may  be  brought  nearer  together,  so  that 
the  current  shall  not  have  to  traverse  so  thick  a  stratum  of 
liquid. 

(2)  The  size  of  the  plates  may  be  increased,  as  this  affords 
the  current,  as  it  were,  a  greater  number  of  possible  paths 
through  the  stratum  of  liquid. 

(3)  The  zincs  of  several  cells  may  be  joined  together,  to 
form,  as  it  were,  one  large  zinc  plate ;  the  coppers  being  also 
joined  to  act  as  one  large  copper  plate.     Suppose  four  similar 
cells  thus  joined  "  in  parallel,"  the  current  has  four  times  the 
available  number  of  paths  by  which  it  can  traverse  the  liquid 
from  zinc  to  copper ;   hence  the  internal  resistance  of  the 
whole  group  will  be  only  \  of  that  of  a  single  cell.     But 
the  E.M.F.  of  them  will  be  no  greater  thus  than  that  of 
one  cell. 

The  current  is  also  affected  by  the  resistances  of  the  wires 
of  the  external  circuit;  and  if  the  external  resistance  be  al- 
ready great,  as  in  telegraphing  through  a  long  line,  it  is  of 
little  use  to  diminish  the  internal  resistance  if  this  is  already 


176  ELECTRICITY  AND   MAGNETISM      [FT.  i.  208 

much  smaller  than  the  resistance  of  the  line  wire.  It  is,  on 
the  contrary,  advantageous  to  increase  the  number  of  cells  in 
series,  though  every  cell  adds  a  little  to  the  total  resistance. 

Example.  —  If  the  line  has  a  resistance  of  1000  ohms,  and  five 
cells  are  used  each  of  which  has  an  E.M.F.  of  I'l  volt  and 
an  internal  resistance  of  3  ohms,  by  Ohm's  Law  the  current 
will  be  5*5  +  1015;  or  0*0054  ampere.  If  now  eight  cells 
in  series  are  used,  though  the  total  resistance  is  thereby  in- 
creased from  1015  to  1024  ohms,  yet  the  E.M.F.  is  increased 
from  5*5  to  8'8  volts,  and  the  current  to  0'0085  ampere. 

208.  Keys,  Switches,  and  Reversers.  —  Various  forms  of 
keys  and  switches  are  used  for  making  and  breaking  the  con- 
nexion of  a  battery  to  a  circuit.  A  key  is  an  appliance  con- 
sisting essentially  of  a  lever  carrying  a  contact  or  contacts, 
generally  used  in  signalling  and  in  testing.  It  is  not  advis- 
able to  leave  a  battery  supplying  current  longer  than  the 
period  of  actual  use  because  of  the  rapid  action  of  polariza- 
tion (Art.  183).  The  simplest  key  (shown  in  Fig.  144,  p. 
208)  consists  of  a  brass  arm  fixed  at  one  end,  the  other  end 
being  sprung  so  as  not  to  make  circuit  with  a  contact  placed 
underneath.  On  depressing  the  arm  the  circuit  is  made, 
while  in  its  normal  position  it  is  broken.  The  Morse  key 
(Fig.  343)  is  a  lever,  held  up  by  a  spring,  which  on  depressing 
disconnects  receiving  instruments  and  transmits  current 
to  the  line.  A  plug  switch  consists  of  two  contacts  separated 
by  a  small  space  which  can  be  connected  by  the  insertion 
of  a  plug.  A  circuit  breaker  (Art.  561)  is  a  switch  which 
is  opened  automatically  when  the  current  or  the  pressure 
exceeds  (or  falls  below)  a  certain  limit. 

It  is  sometimes  necessary  to  reverse  the  direction  of  the 
current  in  a  circuit  when  carrying  out  special  tests  (e.g. 
Art.  393  6).  One  form  of  reverser  operating  with  a  rotary 
motion  is  depicted  in  Fig.  152.  Another  form  consists  of  a 
rocking  contact  piece,  operating  in  mercury  cups,  which  either 
connects  the  battery  direct  to  the  circuit  or  cross-connects 
it  according  to  the  position  of  the  rocking  contacts. 


CH.  in.  209] 


OERSTED'S   DISCOVERY 


177 


LESSON  XVI.  —  Magnetic  Actions  \  of  the   Current 

209.  Oersted's  Discovery.  —  A  connexion  of  some  kind 
between  magnetism  and  electricity  had  long  been  suspected. 
Lightning  had  been  known  to  magnetize  knives  and  other 
objects  of  steel ;  but  almost  all  attempts  to  imitate  these 
effects  by  powerful  charges  of  electricity,  or  by  sending 
currents  of  electricity  through  steel  bars,  had  failed.1  About 
1802  Romagnosi,  of  Trente,  vaguely  observed  that  a  voltaic 
pile  affects  a  compass-needle.  The  true  connexion  between 
magnetism  and  electricity  remained,  however,  to  be  dis- 
covered. 

In  1819,  Oersted,  of  Copenhagen,  showed  that  a  magnet 
needle  tends  to  set  itself  at  right  angles  to  a  wire  carrying 


FIG.  117.  —  Oersted's  Experiment:    Deflexion  of  Needle  by  Current. 

an  electric  current.  He  also  found  that  the  way  in  which 
the  needle  turns,  whether  to  the  right  or  the  left  of  its  usual 
position,  depends  upon  the  position  of  the  wire  that  carries 
the  current  —  whether  it  is  above  or  below  the  needle  — 
and  on  the  direction  in  which  the  current  flows  through  the 
wire. 

His  chief  experiment  is  this :  —  Let  a  magnetic  needle 
be  suspended  on  a  pointed  pivot,  as  in  Fig.  117.  Above 
it,  and  parallel  to  it,  is  held  a  stout  copper  wire,  one  end 

1  Hitherto  in  these  lessons  magnetism  and  electricity  have  been  con- 
sidered separately ;  no  connexion  between  them  has  been  apparent.  The 
student  who  cannot  remember  whether  a  charge  of  electricity  does  or  does 
not  affect  a  magnet,  should  turn  back  to  what  was  said  in  Art.  102,  p.  91. 

N 


178  ELECTRICITY  AND   MAGNETISM    [PT.  i.  210,  211 

of  which  is  joined  to  one  pole  of  a  battery  of  one  or  two  cells. 
The  other  end  of  the  wire  is  then  brought  into  contact  with 
the  other  pole  of  the  battery.  As  soon  as  the  circuit  is  com- 
pleted the  current  flows  through  the  wire  and  the  needle 
turns  briskly  aside.  If  the  current  be  flowing  from  South 
to  North  along  the  wire,  Over  the  needle,  the  north-seeking 
pole  of  the  needle  will  turn  Westwards.  (The  letters  in 
capitals  —  SNOW  —  will  help  the  memory.)  If,  as  in 
Fig.  117,  the  current  flows  from  North  to  South,  Over  the 
needle,  the  needle  will  be  deflected  Eastwards.  If  the  wire 
is,  however,  below  the  needle,  the  motions  will  be  reversed ; 
a  current  flowing  from  North  to  South,  Under  the  needle, 
will  cause  a  deflexion  Westwards. 

210.  Ampere's    Rule.  —  To    keep    these    movements    in 
memory,    Ampere    suggested    the     following    fanciful    but 
useful   rule.     Suppose  a  man  swimming  in  the  wire  with 
the   current,   always  facing   the  needle,    then   the    N-seeking 
pole  of  the  needle  will  be  deflected  towards  his  left  hand. 

For  certain  particular  cases  in  which  a  fixed  magnet 
pole  acts  on  a  movable  circuit,  the  following  converse  to 
Ampere's  Rule  will  be  found  convenient.  Suppose  a  man 
swimming  in  the  wire  with  the  current,  and  that  he  turns 
so  as  to  look  along  the  direction  of  the  lines  of  force  of 
the  pole  (i.e.  as  the  lines  of  force  run,  from  the  pole  if  it 
be  N-seeking,  towards  the  pole  if  it  be  S-seeking),  then  he  and 
the  conducting  wire  with  him  will  be  urged  toward  his  left. 

211.  Corkscrew    Rule.  —  The    following    rule    was    sug- 
gested by  Maxwell.     The  direction  of  the  current  and  that 

of  the  resulting  magnetic  force  are  related  to  one 
another,  as  are  the  rotation  and  the  forward  travel 
of  an  ordinary  (right-handed)  corkscrew.  In 
Fig.  118,  if  the  circle  represents  the  circulation 

FIO.  us. —  Cork-  of  current,  the  arrow  gives  the  direction  of 
the  resulting  magnetic  force.  One  advantage 

of  this  rule  is,  that  it  is  equally  applicable  in  the  other  case. 

If  the  arrow  represents  the  direction  of  the  current  along 


CH.  in.  212]  THE    GALVANOSCOPE  179 

a  straight  wire,  the  circle  will  represent  the  direction  of  the 
resulting  magnetic  force  around  it. 

212.  Galvanoscope.  —  A  little  consideration  will  show 
that  if  a  current  be  carried  below  a  needle  in  one  direction, 
and  then  back  in  the  opposite  direction  above  the  needle, 
by  bending  the  wire  round,  as  in  Fig.  119,  the  forces 
exerted  on  the  needle  by  both  portions  of  the  current 
will  be  in  the  same  direction.  For  let  a  be  the  N-seeking, 
and  b  the  S-seeking,  pole  of  the  suspended  needle,  then 
the  tendency  of  the  current  in  the  lower  part  of  the  wire 
will  be  to  turn  the  needle  so  that  a  comes  towards  the 
observer,  while  b  retreats ;  while  the  current  flowing  above, 
which  also  deflects  the  N-seeking  pole  to  its  left,  will  equally 
urge  a  towards  the  observer,  and  b  from  him.  The  needle 
will  not  stand  out  completely  at  right  angles  to  the  direction 
of  the  wire  conductor,  but  will  take  an  oblique  position. 
The  directive  forces  of  the  earth's  magnetism  are  tending 
to  make  the  needle  point  north-and-south.  The  electric 
current  is  acting  on  the  needle,  tending  to  make  it  set  itself 
west-and-east.  The  resultant  force  will  be 
in  an  oblique  direction  between  these,  and 
will  depend  upon  the  relative  strength  of 
the  two  conflicting  forces.  If  the  current 
is  very  strong  the  needle  will  turn  widely 
round ;  but  could  -only  turn  completely  r? 
to  a  right  angle  if  the  current  were  infinitely 
strong.  If,  however,  the  current  is  feeble 

.,,      '  v  .      FIG.  119.  —  Galvano- 

m  comparison  with  the  directive  magnetic  scope. 

force,  the  needle  will  turn  very  little. 

This  arrangement  will,  therefore,  serve  roughly  as  a 
Galvanoscope  or  indicator  of  currents ;  for  the  movement 
of  the  needle  shows  the  direction  of  the  current,  and  indicates 
whether  it  is  a  strong  or  a  weak  one.  This  apparatus  is  too 
rough  to  detect  very  delicate  currents.  To  obtain  a  more 
sensitive  instrument  there  are  two  possible  courses :  (i.)  in- 
crease the  effective  action  of  the  current  by  carrying  the 


180  ELECTRICITY   AND   MAGNETISM    [PT.  i.  213,  214 

wire  more  than  once  round  the  needle;  (ii.)  decrease  the 
opposing  directive  force  of  the  earth's  magnetism  by  some 
compensating  contrivance. 

213.  Schweigger's   Multiplier.  —  The  first  of  the  above 
suggestions  was  carried  out  by  Schweigger,  who  constructed 
a  multiplier  of  many  turns  of  wire.     A  suitable  frame  of 
wood,  brass,  or  ebonite,  is  prepared  to  receive  the  wire, 
which  must  be  "  insulated,"  or  covered  with  silk,  or  cotton, 
or  indiarubber,  to  prevent  the  separate  turns  of  the  coil  from 
coming  into  contact  with  each  other.     Within  this  frame, 
which  may  be  circular,  elliptical,  or  more  usually  rectangular, 
as  in  Fig.  120,  the  needle  is  suspended ;    the  frame  being 

placed  so  that  the  wires  lie  in  the 
magnetic  meridian.  The  greater 
the  number  of  turns  the  more 
powerful  will  be  the  magnetic 
deflexion  produced  by  the  passage 
of  equal  quantities  of  current. 
But  if  the  wire  is  thin,  or  the  num- 
ber of  turns  of  wire  numerous,  the 
V-  resistance  thereby  offered  to  the 
flow  of  electricity  may  very  greatly 

FIG.  120.  — Schweigger's  Multiplier  J  ,.       ,  . , 

reduce  the  strength  of  the  current. 

The  student  will  grasp  the  importance  of  this  observation 
when  he  has  read  the  chapter  on  Ohm's  Law.  Gumming, 
of  Cambridge,  appears  to  have  been  the  first  to  use  a  coil 
surrounding  a  pivoted  needle  to  measure  the  current.  To 
him  we  owe  the  term  Galvanometer. 

214.  Astatic  Combinations  of  Magnets.  —  The  directive 
force  exercised  by  the  earth's  magnetism  on  a  magnetic 
needle  may  be  reduced  or  obviated  by  one  of  two  methods : 

(a)  [Hauy's  Method.]  By  employing  a  compensating 
magnet.  An  ordinary  long  bar  magnet  laid  in  the  mag- 
netic meridian,  but  with  its  N-seeking  pole  directed  towards 
the  north,  will,  if  placed  horizontally  above  or  below  a 
suspended  magnetic  needle,  tend  to  make  the  needle  set 


CH.  in.  214] 


GALVANOMETERS 


181 


FIG.  121.  —  Astatic  Pair. 


itself  with  its  S-seeking  pole  northwards.  If  near  the 
needle  it  may  overpower  the  directive  force  of  the  earth, 
and  cause  the  needle  to  reverse  its  usual  position.  If  it  is 
far  away,  all  it  can  do  is  to  lessen 
the  directive  force  of  the  earth. 
At  a  certain  distance  the  magnet 
will  just  compensate  this  force,  and 
the  needle  will  be  neutral.  This 
arrangement  for  reducing  the 
earth's  directive  force  is  applied  in 
the  reflecting  galvanometer  shown 
in  Fig.  134,  in  which  the  controlling 
magnet  at  the  top,  curved  in  form 
and  capable  of  adjustment  to  any  height,  affords  a  means 
of  adjusting  the  instrument  to  the  desired  degree  of  sensitive- 
ness by  raising  or  lowering  it. 

(b)  [Nobili's  Method].  By  using  an  astatic  pair  of  mag- 
netic needles.  If  two  magnetized  needles  of  equal  strength 
and  size  are  bound  together  by  a  light  wire  of 
brass,  or  aluminium,  in  reversed  positions,  as 
shown  in  Fig.  121,  the  force  urging  one  to  set 
itself  in  the  magnetic  meridian  is  exactly 
counterbalanced  by  the  force  that  acts  on  the 
other.  Consequently  this  pair  of  needles 
will  remain  -in  any  position  in  which  it  is  set, 
and  is  independent  of  the  earth's  magnetism. 
Such  a  combination  is  known  as  an  astatic 
pair.  It  is,  however,  difficult  in  practice  to 
obtain  a  perfectly  astatic  pair,  since  it  is  not  easy  to  magnet- 
ize two  needles  exactly  to  equal  strength,  nor  is  it  easy  to 
fix  them  perfectly  parallel  to  one  another.  Such  an  astatic 
pair  is,  however,  readily  deflected  by  a  current  flowing  in  a 
wire  coiled  around  one  of  the  needles ;  for,  as  shown  in  Fig. 
122,  the  current  which  flows  above  one  needle  and  below 
the  other  will  urge  both  in  the  same  direction,  because  they 
are  already  in  reversed  positions.  It  is  even  possible  to  go 


FIG.  122.  —  Astatic 
Pair. 


182 


ELECTRICITY  AND   MAGNETISM       [PT.  i.  215 


T 


FIG.  123.  —  Verti- 
cal Astatic  Pair. 


further,  and  to  carry  the  wire  round  both  needles,  winding 
the  coil  around  the  upper  in  the  opposite  sense  to  that  in 
which  the  coil  is  wound  round  the  lower  needle.     Several 
other    astatic    combinations    are    possible.     For    example, 
two  needles  may  be  lightly  braced  together 
vertically,  as  in  Fig.  123,  with 
poles  reversed  and  suspended  @) 

to  turn.  Or  the  astatic  com- 
bination (Broca's)  of  Fig.  124, 
with  consequent  poles  (Art. 
122)  at  the  middle  points,  may 
be  used. 

Nobili  applied  the  astatic  ar- 
rangement  of   needles  to  the 
multiplying  coils  of  Schweigger, 
and   thus  constructed  a  very  FlYstatic~pair°Ca'3 
sensitive    instrument,    the 

Astatic  Galvanometer,  shown  in  Fig.  131.  The  special  forms 
of  galvanometer  adapted  for  the  commercial  measurement 
of  currents  are  described  in  the  next  Lesson. 

215.  Magnetic  Field  due  to  Current ;  Magnetic  Whirls.  - 
Arago  found  that  if  a  current  be  passed  through  a  piece  of 
copper  wire  it  becomes  capable  of  attracting  iron  filings  to 
it  so  long  as  the  current  flows.  These  filings  set  themselves 
tangentially  to  the  wire,  and  cling  around  it,  but  drop  off 
when  the  circuit  is  broken.  There  is,  then,  a  magnetic 
"  field  "  around  the  wire  which  carries  the  current ;  and  it 
is  important  to  know  how  the  lines  of  force  are  distributed 
in  this  field. 

Let  the  central  spot  in  Fig.  125  represent  an  imagined 
cross-section  of  the  wire,  and  let  us  suppose  the  current 
to  be  flowing  in  through  the  paper  at  that  point.  Then, 
by  the  corkscrew  rule,  a  magnet  needle  placed  near 
the  side  of  the  wire  will  tend  to  set  itself  at  right  angles 
to  the  current,  in  positions  such  as  those  shown  in  the 
figure,  with  the  N-pole  pointing  in  the  clockwise  direc- 


CH.  in.  215] 


MAGNETIC   WHIRLS 


183 


oat 


V? 


FIG.  125.  FIG.  126. 

Action  of  Vertical  Wire  on  Needles. 


tion.1  In  fact  the  tendency  would  be  to  urge  the  N-seeking 
pole  round  the  conductor  in  the  same  way  as  the  hands  of  a 
clock  move ;  while  the  S-seeking  pole  would  be  urged  in 
the  opposite  cyclic  direction  to  that  of  the  hands  of  a  clock. 
If  the  current  is  reversed,  and  is  N  N 

regarded  as  flowing  towards  the    $^r  ^  ^~~  ~ 

reader,  i.e.  coming  up  out  of  the  *     .•  /     •      \ 

plane  of  the  paper,  as  in  the  dia-  \  K ''  J 
gram  of  Fig.  126,  then  the  motions 
would  be  just  in  the  reverse  sense. 
It  would  seem  from  this  as  if  a 
N-seeking  pole  of  a  magnet  ought  to  revolve  continuously 
round  and  round  a  current ;  but  as  we  cannot  obtain  a  mag- 
net with  one  pole  only,  and  as  the  S-seeking  pole  is  urged  in 
an  opposite  direction,  all  that  occurs  is  that  the  needle  sets 
itself  as  a  tangent  to  a  circular  curve  surrounding  the  con- 
ductor. The  field  surrounding  the  conductor  consists  in  fact 
of  a  sort  of  enveloping  magnetic  whirl 
all  along  it,  the  whirl  being  strong  near 
the  wire  and  weaker  farther  away.  This 
is  what  Oersted  meant  when  he  de- 
scribed the  electric  current  as  acting  "  in 
a  revolving  manner  "  upon  the  mag- 
netic needle.  The  field  of  force,  with 
its  circular  lines  surrounding  a  current 
flowing  in  a  straight  conductor,  can  be 
examined  experimentally  with  iron  filings  in  the  following 
way  :  A  card  is  placed  horizontally  and  a  stout  copper  wire  is 
passed  vertically  through  a  hole  in  it  (Fig.  127).  Iron  filings 
are  sifted  over  the  card  (as  described  in  Art.  121),  and  a  strong 
current  from  three  or  four  large  cells  is  passed  through  the 

1  The  student  may  apply  Ampere's  rule  to  this  case,  and  to  others  which 
follow.  Thus,  supposing  himself  to  dive  head  foremost  into  the  page  at 
the  point  marked  in,  and  to  turn  round  so  as  to  face  each  of  the  magnets 
in  succession,  he  will  find  each  N-pole  directed  to  his  left.  In  diagram  126 
he  must  conceive  himself  as  coming  up  out  of  the  spot  where  the  current  is 
flowing  out. 


FIG.'  127.  —  Field  due  to 
"  Vertical  Wire. 


184  ELECTRICITY   AND   MAGNETISM       [PT.  i.  216 

wire.  On  tapping  the  card  gently  the  filings  near  the  wire 
set  themselves  in  concentric  circles  round  it.  It  is  because 
of  this  surrounding  field  that  two  conductors  can  apparently 
act  on  one  another  at  a  distance.  If  both  currents  are  flow- 
ing in  the  same  direction,  their  magnetic  fields  tend  to  merge, 
and  the  resulting  stress  in  the  medium  tends  to  drag  them 
together  with  an  apparent  attraction.  If  the  currents  are 
flowing  in  opposite  directions  the  stresses  in  the  intervening 
magnetic  field  tend  to  thrust  them  apart  (see  also  Art.  420). 

It  is  known  that  energy  has  to  be  spent  in  producing 
any  magnetic  field.  When  a  current  is  turned  on  in  a 
wire  the  magnetic  field  grows  around  the  wire,  some  of  the 
energy  of  the  battery  being  used  during  the  growth  of  the 
current  for  that  purpose.  One  reason  why  electric  currents 
do  not  instantly  rise  to  their  final  value  (Art.  505)  is  the  re- 
active effect  of  this  surrounding  magnetic  field.  No  current 
can  exist  without  this  surrounding  magnetic  field.  Indeed  it 
is  impossible  to  refute  the  proposition  that  what  we  measure 
as  an  electric  current  in  a.  wire  really  is  this  external  magnetic 
whirl. 

216.  Equivalent  Magnetic  Shell :  Ampere's  Theorem.  — 
For  many  purposes  the  following  way  of  regarding  the  mag- 
netic action  of  electric  currents  is  more  convenient  than  the 
preceding.  Suppose  we  take  a  battery  and  connect  its 
terminals  by  a  circuit  of  wire,  and  that  a  portion  of  the  circuit 
be  twisted,  as  in  Fig.  128,  into  a  looped  curve,  it  will  be 
found  that  the  entire  space  enclosed  by  the  loop  possesses 
magnetic  properties.  In  our  figure  the  current  is  supposed 
to  be  flowing  round  the  loop,  as  viewed  from  above,  in  the 
same  direction  as  the  hands  of  a  clock  move  round ;  an  im- 
aginary man  swimming  round  the  circuit  and  always  facing 
towards  the  centre  would  have  his  left  side  down.  Then 
by  the  corkscrew  rule  a  N-seeking  pole  would  be  urged 
downwards  through  the  loop,  while  a  S-seeking  pole  would  be 
urged  upwards.  In  fact  the  space  enclosed  by  the  loop  of 
the  circuit  behaves  like  a  magnetic  shell  (see  Art.  120),  having 


CH.  m.  217] 


MAGNETIC   WHIRLS 


185 


its  upper  face  of  S-seeking  magnetism,  and  its  lower  face  of 
N-seeking  magnetism.  A  closed  voltaic  circuit  is  equivalent 
to  a  magnetic  shell  whose  edges  coincide  in  position  with  the 
circuit,  the  shell  being  of  such  a  strength  that  the  number  of 
its  lines  of  force  is  the  same  as  that  of  the  lines  of  force  due 
to  the  current  in  the  circuit.  The  circuit  acts  on  a  magnet, 
attracting  or  repelling  it,  and  being  attracted  or  repelled  by  it, 
exactly  as  its  equivalent  magnetic  shell  would  do.  Also,  the 


FIG.  128.  —  Magnetic  Properties  of  Conductor. 

circuit  itself,  when  placed  in  a  magnetic  field,  experiences  the 
same  force  as  its  equivalent  magnetic  shell  would  do. 

217.  Maxwell's  Rule.  —  Clerk  Maxwell  gave  the  follow- 
ing rule  for  determining  the  mutual  action  of  a  circuit  and  a 
magnet  placed  near  it.  Every  portion  of  the  circuit  is  acted 
upon  by  a  force  urging  it  in  such  a  direction  as  to  make  it 
enclose  within  its  embrace  the  greatest  possible  number  of  lines 
of  force.  If  the  circuit  is  fixed  and  the  magnet  movable, 
then  the  force  acting  on  the  magnet  will  also  be  such  as  to 
tend  to  make  the  number  of  lines  of  force  that  pass  through 
the  circuit  a  maximum  (see  also  Art.  376). 

This  is  but  one  case  of  the  still  more  general  law  governing 
every  part  of  every  electromagnetic  system,  viz. :  Every 
electromagnetic  system  tends  so  to  change  the  configuration  of 
its  parts  as  to  make  the  interlinkage  of  magnetic  lines  with  the 
exciting  circuit  a  maximum  (Art.  409). 


186 


ELECTRICITY  AND   MAGNETISM    [PT.  i.  218,  219 


FIG.  129.  —  De  la  Rive's  Floating  Coil. 


218.  De  la  Rive's  Floating  Coil.  —  The  preceding  remarks 
may  be  illustrated  experimentally  by  the  aid  of  a  little  floating 

circuit.  A  plate  of  zinc  and 
one  of  copper  (see  Fig.  129) 
are  fixed  side  by  side  in  a  large 
cork,  and  connected  above  by 
a  coil  of  several  turns  of  cov- 
ered copper  wire.  This  is 
floated  upon  a  dish  containing 
dilute  sulphuric  acid.  If  one 
pole  of  a  bar  magnet  be  held 
towards  the  ring  it  will  be 
attracted  or  repelled  accord- 
ing to  the  pole  employed. 
The  floating  circuit  will  so  move  as  to  make  the  flux  of  mag- 
netic lines  through  the  coil  a  maximum.  If  the  S-pole  of 
the  magnet  be  presented  to  that  face  of  the  ring  which  acts 
as  a  S-seeking  pole  (viz.  that  face  round  which  the  current 
is  flowing  in  a  clockwise  direction),  it  will  repel  it.  If  the  pole 
be  thrust  right  into  the  ring,  and  then  held  still,  the  battery 
will  be  strongly  repelled,  will  draw  itself  off,  float  away,  turn 
round  so  as  to  present  toward  the  S-pole  of  the  magnet  its 
N-seeking  face,  will  then  be  attracted  up,  and  will  thread 
itself  on  to  the  magnet  up  to  the  middle,  in  which  position 
as  many  magnetic  lines  as  possible  traverse  the  area  of  the 
ring,  and  link  themselves  with  the  current. 

Two  circuits  traversed  by  currents  attract  and  repel  one 
another  just  as  two  magnetic  shells  would  do. 

A  piece  of  iron  or  steel  can  be  magnetized  by  causing  a 
current  to  circulate  around  it  in  a  spiral  wire.  This  intro- 
duces the  subject  of  electromagnets,  which  is  dealt  with  in 
Arts.  411  to  417,  p.  376. 

219.  Strength  of   the   Current  in   Magnetic   Measure.  — 
When  a  current  thus  acts  on  a  magnet  pole  near  it,  the  force 
/  which  it  exerts  will  be  proportional  to  the  strength  i  of  the 
current,  and  proportional  also  to  the  strength  m  of  the  magnet 


CH.  in.  220]  UNIT   OF   CURRENT  187 

pole,  and  to  the  length  I  of  the  wire  employed :  the  force  ex- 
erted between  each  element  of  the  circuit  and  the  pole  will  also 
vary  inversely  as  the  square  of  the  distance  r  between  them. 
If  the  wire  is  looped  into  a  circular  coil  with  the  magnet  pole 
at  the  centre,  so  that  each  portion  of  the  circuit  is  approxi- 
mately at  the  same  distance  from  the  pole,  /  =  —  dynes. 
Suppose  the  wire  looped  up  into  a  circle  round  the  magnet 
pole,  then  I  =  2irr,  and  /  =  -  -  m  dynes.  Suppose  also  that 

the  circle  is  of  one  centimetre  radius,  and  that  the  magnet 
pole  is  of  strength  of  one  unit  (see  Art.  379),  then  the  force 

exerted  by  the  current  of  strength  i  will  be  —  X  1,  or  2  id 

dynes.  In  order,  therefore,  that  a  current  of  strength  i 
should  exert  a  force  of  i  dynes  on  the  unit  pole,  one  must  con- 
sider the  current  as  travelling  round  only  — -  part  of  the 

2?r 

circle,  or  round  a  portion  of  the  circumference  equal  in  length 
to  the  radius. 

220.  Unit  of  Current.  —  A  current  is  said  to  have  a 
strength  of  one  "  absolute  "  unit  when  it  is  such  that  if 
one  centimetre  length  of  the  circuit  is  bent  into  an  arc  of 
one  centimetre  radius,  the  current  in  it  exerts  a  force  of  one 
dyne  on  a  magnet-pole  of  unit  strength  placed  at 
the  centre  of  the  arc.  The  practical  unit  of  "one 
ampere  "  is  only  T^  of  this  theoretical  unit  (see 
also  Art.  381). 

If  the  wire,  instead  of  being  looped  into  a  coil, 
is  straight  and  of  indefinite  length,  the  force  which 
the  current  in  it  exerts  upon  a  pole  of  strength  m 
placed  at  point  P  near  it  will  be  found  to  vary  in- 
versely as  the  simple  distance  (not  as  the  square),      FlGl  13°- 
and  the  pole  will  tend  to  move  at  right  angles  both  to  the  wire 
and  to  the  line  OP.     In  Fig.  130  the  descending   current 
will  (according  to  the  corkscrew  rule  above)  tend  to  drive 


188  ELECTRICITY  AND   MAGNETISM       [PT.  i.  221 

a  N-pole  at  P  towards  the  •  spectator.  If  the  current  is  i 
amperes  the  force  (in  dynes)  on  the  pole  of  m  units  will  (see 
Art.  371)'  be 

/  =  2  mi/10  r 

Example.  —  The  force  exerted  by  a  current  of  60  amperes  in  a 
long  straight  conductor  upon  a  pole  of  200  units  placed 
2  centimetres  away  from  it  will  be  1200  dynes,  or  (divid- 
ing by  g  =  981)  about  1-22  grammes'  weight. 

LESSON  XVII.  —  Galvanometers 

221.  The  term  Galvanometer  is  applied  to  an  instrument 
for  measuring  the  strength  of  electric  currents  by  means  of 
their  electromagnetic  action.  There  are  two  general  classes 
of  Galvanometers:  (1)  those  in  which  the  current  flowing 
in  a  fixed  coil  of  wire  causes  the  deflexion  of  a  pivoted  or  sus- 
pended magnetic  needle;  (2)  those  in  which  the  current 
flowing  in  a  movable  coil  suspended  between  the  poles  of  a 
•fixed  magnet  causes  the  coil  to  turn.  There  is  a  third  kind 
of  instrument  (called,  for  distinction  eledrodynamometer,  see 
Art.  425),  in  which  both  the  moving  part  and  the  fixed  part 
are  coils.  These  last  are  used  chiefly  for  alternating-currents 
(see  Lesson  XLIV,  p.  505). 

The  simple  arrangement  described  in  Art.  212  was  termed 
a  "  galvanoscope,"  or  current  indicator,  but  it  could  not 
rightly  be  termed  a  "  galvanometer  "  or  current  measurer, 
because  its  indications  were  only  qualitative,  not  quantita- 
tive. The  indications  of  the  needle  did  not  afford  accurate 
knowledge  as  to  the  exact  strength  of  current  flowing  through 
the  instrument.  A  good  galvanometer  must  fulfil  the  essen- 
tial condition  that  its  readings  shall  really  measure  the 
strength  of  the  current  in  some  certain  way.  It  should  also 
be  adapted  to  the  sort  of  current  for  which  it  is  to  be  used. 
The  galvanometer  adapted  for  measuring  very  small  currents 
(say  a  current  of  only  one  or  two  millionth  parts  of  an  ampere) 
'will  not  be  suitable  for  measuring  strong  currents,  such  as 
are  used  in  electric  lighting  or  electro-plating.  Large  cur- 
rents need  thick  wires;  and  a  coil  of  few  turns  will  suffice. 


CH.  in.  222]'  METHODS   OF   CONTROL  189 

If  very  small  currents  are  to  turn  the  needle  they  must  circu- 
late hundreds  or  thousands  of  times  around  it;  for  these, 
therefore,  a  coil  of  many  turns  is  appropriate,  and  the  wire 
may  be  a  very  fine  one.  Moreover,  if  the  current  to  be 
measured  has  already  passed  through  a  circuit  of  great  re- 
sistance (as,  for  example,  some  miles  of  telegraph  wire),  a 
galvanometer  whose  coil  is  a  short  one,  consisting  only  of  a 
few  turns  of  wire,  will  be  of  no  use,  and  a  long-coil  galva- 
nometer must  be  employed  with  many  hundreds  or  even  thou- 
sands of  turns  of  insulated  wire  round  the  needle.  The  reason 
of  this  is  explained  hereafter  (Art.  440).  Hence  it  will  be 
seen  that  different  styles  of  instrument  are  needed  for  differ- 
ent kinds  of  use;  but  of  all  it  is  required  that  they  should 
afford  quantitative  measurements,  that  they  should  be  suffi- 
ciently sensitive  for  the  current  that  is  to  be  measured,  and 
carry  that  current  without  overheating. 

222.  Methods  of  Control.  —  In  all  instruments,  whether 
the  moving  part  be  a  magnet  or  a  coil,  some  controlling  force 
is  needful,  otherwise  the  very  smallest  current  would  turn  the 
index  completely  about.  If  small  currents  are  to  produce 
a  small  deflexion,  and  larger  currents  a  larger,  there  must  be 
forces  tending  to  control.  Several  means  of  control  may  be 
used.  These  are  :  — 

(a)  Earth7 s  Magnetic  Force.  —  When  the  needle  is  hung 
on  a  pivot  or  fibre,  the  earth's  magnetic  force  tries  to  bring 
it  back  into  the  magnetic   meridian.     This  is  the    usual 
method  in  galvanometers  with  moving  needles. 

(b)  Torsion  of  Wire.  —  The  moving  part  in  turning  twists 
the  suspending  wire,  which  then  tries  to  untwist,  with  a  .force 
which  increases  as  the  angle  of  deflexion.     This  method  is 
usual  in   galvanometers   with    suspended    coils.      In    some 
instruments  a  coiled  hair-spring  is  used. 

(c)  Gravity.  —  If  the  needle  is  pivoted  on  trunnions  to 
move  in  a  vertical  plane,  it  may  be  weighted  at  one  end. 

(d)  Permanent    Magnet    Control.  —  To    render    a    needle 
instrument  independent  of  position,   it  may  be   arranged 


190  ELECTRICITY   AND    MAGNETISM       [PT.  i.  223 

with  a  powerful  external  steel  magnet  to  bring  the'  needle 

back  to  zero.     No   '  absolute  '  measurements  are  possible 

with  these  instruments,   as  their  readings   depend  on  the 

strength  of  the  controlling  magnet. 

(e)  Bifilar  Suspension.  —  A  needle  or  coil  hung  by  two 

parallel  threads  tends  by  gravity  to  return  to  its  initial  position. 
To  make  an  instrument  very  sensitive  the  control  must 

be  weakened  as  much  as  possible. 

223.    Methods  of  Observation.  —  There  are  the  following 

methods  of  using  galvanometers  in  making  observations :  — 
(i.)  Deflexion  Method.  —  The  angle  through  which  the 
moving  part  (whether  needle  or  coil)  is  deflected 
is  read  off  on  a  scale,  by  pointer  or  reflected 
beam  of  light,  when  the  moving  part  has  come 
to  rest.  This  is  the  most  usual  method, 
(ii.)  Torsion  Method.  —  The  moving  part  is  suspended 
by  a  wire  from  a  torsion  head,  which  is  turned 
round  until  the  index  is  brought  back  to 
zero;  the  controlling  force  then  balancing  the 
deflecting  force.  In  this  case  one  reads  off  the 
angle  through  which  the  torsion  head  has  been 
turned  (see  Torsion  Balance,  Art.  134,  p.  111). 
This  very  accurate  method,  due  to  Ohm,  is  used 
in  Siemens'  electrodynamometer  (Art.  426). 
(iii.)  First  Swing  Method.  —  Instead  of  waiting  for 
moving  part  to  come  to  rest  the  first  swing  may 
be  observed.  This  method,  which  is  the  only 
one  practicable  for  sudden  discharges,  or  for 
transient  currents,  is  called  the  ballistic  method 
(see  Art.  234).  If  the  moving  part  is  not  damped 
in  its  motion  the  first  swing  on  turning  on  a  battery 
current  is  exactly  twice  the  angle  at  which  the 
deflexion  settles  down. 

(iv.)  Oscillation  Method.  —  Instead  of  observing  deflexion, 
the  time  of  oscillation  of  the  needle  may  be  ob- 
served, the  coil  being  in  this  method  set  at  right 


CH.  in.  224] 


ASTATIC    GALVANOMETER 


191 


angles  to  the  magnetic  meridian.  Allowance 
must  be  made,  as  in  Art.  135,  for  the  earth's 
magnetism. 

(v.)  Cumulative  Method.  —  For  very  minute  currents 
a  method  is  sometimes  adopted  to  get  up  a  meas- 
urable swing  by  reversing  the  current  (by  hand) 
as  the  needle  swings  through  zero.  Sometimes  a 
rotating  commutator  of  special  construction  is 
employed  to  produce,  and  accumulate,  the  succes- 
sive impulses. 

(vi.)  Null  Methods.  —  In  many  cases  connexions  are 
used  (Wheatstone's  "  Bridge/'  "  Differential  Gal- 
vanometers," etc.)  of  such  a  kind  that  when  the 
conditions  of  electrical  equilibrium  are  attained 
no  current  will  flow  through  the  galvanometer  in 
the  circuit.  Such  methods,  which  are  generally 
exceedingly  accurate,  are  known  as  null  methods. 
For  such  methods  sensitive  galvanometers  are 
applicable,  but  the  graduation  of  their  scale  is 
unimportant. 

224.  Nobili's  Astatic  Galvanometer.  —  The  instrument 
constructed  by  Nobili,  consisting  of  an  astatic  pair  of  needles 
delicately  hung,  so  that  the 
lower  one  lay  within  a  coil  of 
wire  wound  upon  an  ivory 
frame  (Fig.  131),  was  for  long 
the  favourite  form  of  sensitive 
galvanometer.  The  needles 
of  this  instrument,  being  inde- 
pendent of  the  earth's  magnet- 
ism, take  their  position  in  obe- 
dience to  the  torsion  of  the  fibre 
by  which  they  are  hung.  The 
frame  on  which  the  coil  is 
wound  must  be  set  carefully 

,         FIG.  131.  — Nobili's  Astatic  Galva- 

parallel  to  the  needles;     and  nometer. 


192  ELECTRICITY   AND   MAGNETISM       [PT.  i.  225 

three  screw  feet  serve  to  adjust  the  base  of  the  instrument 
level.  Protection  against  currents  of  air  is  afforded  by  a  glass 
shade.  When  a  current  is  sent  through  the  wire  coils  the 
needles  move  to  right  or  left  over  a  graduated  circle.  When 
the  deflexions  are  small  (i.e.  less  than  10°  or  15°)  they  are  very 
nearly  proportional  to  the  strength  of  the  currents  that 
produce  them.  Thus,  if  a  current  produces  a  deflexion  of  6° 
it  is  known  to  be  approximately  three  times  as  strong  as  a 
current  which  only  turns  the  needle  through  2°.  But  this 
approximate  proportion  ceases  to  be  true  if  the  deflexion  is 
more  than  15°  or  20° ;  for  then  the  needle  is  not  acted  upon  so 
advantageously  by  the  current,  since  the  poles  are  no  longer 
within  the  coils,  but  are  protruding  at  the  side,  and,  more- 
over, the  needle  being  oblique  to  the  force  acting  on  it,  part 
only  of  the  force  is  turning  it  against  the  directive  force  of  the 
fibre ;  the  other  part  of  the  force  is  uselessly  pulling  or  push- 
ing the  needle  along  its  length.  It  is,  however,  possible  to 
calibrate  the  galvanometer  —  that  is,  to  ascertain  by  special 
measurements,  or  by  comparison  with  a  standard  instrument, 
to  what  strengths  of  current  particular  amounts  of  deflexion 
correspond.  Thus,  suppose  it  once  known  that  a  deflexion 
of  32°  on  a  particular  galvanometer  is  produced  by  a  current 
of  TTO"  °f  an  ampere,  then  a  current  of  that  strength  will 
always  produce  on  that  instrument  the  same  deflexion, 
unless  from  any  accident  the  controlling  force  has  been 
altered. 

225.  The  Tangent  Galvanometer.  —  It  is  not  —  for  the 
reasons  mentioned  above  —  possible  to  construct  a  gal- 
vanometer in  which  the  angle  (as  measured  in  degrees  of  arc) 
through  which  the  needle  is  deflected  is  proportional  through- 
out its  whole  range  to  the  strength  of  the  current.  But  it  is 
possible  to  construct  a  very  simple  galvanometer  in  which 
the  tangent1  of  the  angle  of  deflexion  shall  be  accurately 
proportional  to  the  strength  of  the  current.  The  essential 
feature  of  all  tangent  galvanometers  is  that  while  the  coil  is 

1  See  note  on  "Ways  of  Reckoning  Angles,"  p.  127. 


CH.  in.  2251         TANGENT   GALVANOMETER 


193 


a  large  open  ring  the  needle  is  relatively  very  small.  Fig.  132 
shows  a  form  of  Tangent  Galvanometer  suitable  for  large 
currents.  The  coil  of  this  instrument  consists  of  a  simple 
circle  of  stout  copper  wire  from  10  to  15  inches  in  diameter. 
Other  tangent  galvanometers,  intended  to  measure  small 
currents,  have  many  turns  of  fine  wire  wound  upon  a  large 
open  wooden  ring.  At  the  centre  is  delicately  suspended  a 
magnetized  steel  needle  less  than  an  inch  in  length,  and  usu- 
ally furnished  with  a  light 
index  of  aluminium.  The 
instrument  is  adjusted 
by  setting  the  coil  in  the 
magnetic  meridian,  the 
small  needle  lying  then 
in  the  plane  of  the  coil. 

The  magnetic  field  due 
to  a  current  passing  in 
the  coil  is  not  uniform 
and  normal  to  the  plane 
of  the  coil  except  in  the 
region  near  the  centre  of 
the  coil ;  and  a  consider- 
able error  may  be  intro- 
duced if  the  needle  is  so 
long  that  its  ends  are  in 

the  irregular  parts  of  the  field.  If  the  radius  of  the  circle 
is  large  and  the  needle  short,  its  ends  will  never  be  far  from 
the  centre  of  the  coil,  and  the  needle  may  be  considered 
as  being  always  in  a  uniform  field,  the  direction  of  which  is 
normal  to  the  plane  of  the  coil. 

Several  devices  have  been  adopted  to  ensure  greater  uni- 
formity of  field.  Helmholtz  designed  an  instrument  with 
two  equal  circular  coils  placed  parallel  to  one  another  at  a 
distance  apart  equal  to  their  common  radius;  the  needle 
being  suspended  symmetrically  between  them.  A  yet  more 
exact  result  is  attained  by  placing  three  coils  parallel  to  each 


FIG.  132.  —  Tangent  Galvanometer. 


194  ELECTRICITY   AND   MAGNETISM       [PT.  i.  225 

other,  so  that  all  three  lie  on  the  surface  of  a  sphere  at  the 
centre  of  which  the  needle  is  suspended. 

Whatever  the  magnetic  force  which  the  current  in  the 
coil  can  exert  on  the  needle,  it  will  act  in  a  direction  normal 
to  the  plane  of  the  coil,  and  therefore  at  right  angles  to  the 
earth's  magnetic  force  (provided  the  instrument  has  been 
properly  adjusted  by  setting  the  coil  in  the  magnetic  merid- 
ian). Since  the  two  magnetic  forces  —  the  controlling  force 
of  the  earth  and  the  deflecting  force  of  the  current  —  act  at 
right  angles  to  one  another,  the  action  of  the  current  will  not 
be  measured  by  equal  degrees  marked  out  around  a  circle, 
but  will  be  measured  by  equal  divisions  along  a  tangent  line, 
as  shown  below.  Now,  it  was  proved  in  Art.  139  that>  the 
magnetic  force  which,  acting  at  right  angles  to  the  meridian, 
produces  on  a  magnetic  needle  the  deflexion  $  is  equal  to  the 
horizontal  force  of  the  earth's  magnetism  at  that  place  mul- 
tiplied by  the  tangent  of  the  angle  of  deflexion.  Hence  a 
current  flowing  in  the  coil  will  turn  the  needle  aside  through 
an  angle  such  that  the  tangent  of  the  angle  of  deflexion  is  pro- 
portional to  the  strength  of  the  current. 

Example.  —  Suppose  a  certain  battery  gave  a  deflexion  of 
15°  on  a  tangent  galvanometer,  and  another  battery 
yielding  a  stronger  current  gave  a  deflexion  of  30°.  The 
strengths  of  the  currents  are  not  in  the  proportion  of  1 5  :  30, 
but  in  the  proportion  of  tan  15°  to  tan  30°.  These  values 
must  be  obtained  from  a  table  of  natural  tangents  like 
that  given  in  Appendix  A,  from  which  it  will  be  seen 
that  the  ratio  between  the  strengths  of  the  currents  is 
•268  :  '577,  or  about  10  :  22. 

Or,  more  generally,  if  current  i  produces  deflexion  St  and  current 
i'  deflexion  5',  then 

i:i'  =  tan  5' :  tan  5'. 

To  obviate  reference  to  a  table  of  figures,  the  circular 
scale  of  the  instrument  is  sometimes  graduated  into  tangent 
values  instead  of  being  divided  into  equal  degrees  of  arc. 
Let  a  tangent  OT  be  drawn  to  the  circle,  as  in  Fig.  133,  and 
along  this  line  let  any  number  of  equal  divisions  be  set  off, 


CH.  in.  226] 


TANGENT   SCALES 


195 


beginning  at  O.  From  these  points  draw  back  to  the  cen- 
tre. The  circle  will  thus  be  divided  into  a  number  of 
pieces,  of  which  those  near  O  are  nearly  equal,  but  which 
get  smaller  and  smaller  away  from  O.  These  unequal  pieces 
correspond  to  equal  increments  of  the  tangent.  If  the 
scale  were  divided  thus,  the  readings  would  be  proportional 
to  the  tangents.  It  is,  however,  harder  to  divide  an  arc  into 
tangent  lines  with  accuracy  than  to  divide  it  into  equal 


FIG.  133.  —  Tangent  Scale. 

degrees ;    hence  this  graduation,  though  convenient,  is  not 
used  where  great  accuracy  is  needed. 

226.  Absolute  Measure  of  Current  by  Tangent  Galva- 
nometer. —  The  strength  of  a  current  may  be  determined 
in  "  absolute  "  units  by  the  aid  of  the  tangent  galvanometer 
if  the  "  constants  "  of  the  instrument  are  known.  The  tan- 
gent of  the  angle  of  deflexion  represents  (see  Art.  139)  the 
ratio  between  the  magnetic  force  due  to  the  current  and  the 
horizontal  component  of  the  earth's  magnetic  force.  Both 
these  forces  act  on  the  needle,  and  depend  equally  upon  the 
magnetic  moment  of  the  needle,  which,  therefore,  we  need  not 
know  for  this  purpose.  We  know  that  the  force  exerted  by 
the  current  at  centre  of  the  coil  is  proportional  to  the  hori- 
zontal force  of  the  earth's  magnetism  multiplied  by  the  tan- 
gent of  the  angle  of  deflexion.  These  two  quantities  can  be 
found  from  the  tables,  and  from  them  we  calculate  the  ab- 
solute value  of  the  current  as  follows  :  —  Let  r  represent  the 
radius  of  the  galvanometer  coil  (measured  in  centimetres) ; 
its  total  length  (if  of  one  turn  only)  is  2irr.  The  distance 
from  the  centre  to  all  parts  of  the  coil  is  of  course  r.  From 


196  ELECTRICITY   AND   MAGNETISM      [PT.'I.  227 

our  definition  of  the  absolute  unit  of  current  (Art.  220), 
it  follows  that 

i  X  -y  =  force  (in  dynes)  at  centre, 
or  i  X  —  =  H  •  tan  5, 

where  H  is  the  horizontal  component  of  magnetism  at  the 
place. 

Hence  i  =  — •  H  •  tan  5. 

27T 

The  quantity  2  w/r,  or  2  irn/r  if  the  coil  has  n  turns,  is 
sometimes  called  the  "  constant  "  or  the  "  principal  con- 
stant "  of  the  galvanometer  and  denoted  by  the  symbol  G. 
Hence  the  value  of  the  current  in  absolute  (electromagnetic) 
units  l  will  be  expressed  as 

i  =  TT  tan  6. 

U 

The  constant  G  represents  the  strength  of  field  produced 
at  the  centre  of  the  coil  by  unit  current. 

227.  Sine  Galvanometer.  —  The  disadvantage  of  the 
tangent  galvanometer  just  described  is  that  it  is  not  very 
sensitive,  because  the  coil  is  necessarily  very  large  as  com- 
pared with  the  needle,  and  therefore  far  away  from  it.  A 
galvanometer  with  a  smaller  coil  or  a  longer  needle  cannot 
be  used  as  a  tangent  galvanometer,  though  it  would  be  more 
sensitive.  Any  sensitive  galvanometer  in  which  the  needle 
is  directed  by  the  earth's  magnetism  can,  however,  be  used 
as  a  Sine  Galvanometer,  provided  the  frame  on  which  the 
coils  are  wound  is  capable  of  being  turned  round  a  central 
axis.  When  the  instrument  is  so  constructed,  the  following 
method  of  measuring  currents  is  adopted.  The  coils  are  first 
set  parallel  to  the  needle  (i.e.  in  the  magnetic  meridian) ;  the 
current  is  then  sent  through  it,  producing  a  deflexion ;  the 

1  The  student  will  remember  (Arts.  220  and  381)  that  the  practical  unit 
of  current  which  we  call  "one  ampere"  is  only  ?s  of  one  "absolute"  unit 
of  the  centimetre-gramme-second  system. 


CH.  in.  228]  MIRROR   GALVANOMETER  197 

coil  itself  is  rotated  round  in  the  same  sense,  and,  if  turned 
round  through  a  wide  enough  angle,  will  overtake l  the 
needle,  which  will  once  more  lie  parallel  to  the  coil. 
In  this  position  two  forces  are  acting  on  the  needle :  the 
directive  force  of  the  earth's  magnetism  acting  along  the 
magnetic  meridian,  and  the  force  due  to  the  current  pass- 
ing in  the  coil,  which  tends  to  thrust  the  poles  of  the 
needle  out  at  right  angles ;  in  fact  there  is  a  "  couple  " 
which  exactly  balances  the  "  couple  "  due  to  terrestrial  mag- 
netism. Now  it  was  shown  in  the  Lesson  on  the  Laws  of 
Magnetic  Force  (Art.  138)  that  when  a  needle  is  deflected  the 
"  moment  "  of  the  couple  is  proportional  to  the  sine  of  the 
angle  of  deflexion.  Hence  in  the  sine  galvanometer,  when 
the  coil  has  been  turned  round  so  that  the  needle  once  more 
lies  along  it,  the  strength  of  the  current  in  the  coil  is  proportional 
to  the  sine  of  the  angle  through  which  the  coil  has  been  turned.2 

228.  The  Mirror  Galvanometer.  —  When  a  galvanometer 
of  great  delicacy  is  needed,  the  moving  parts  must  be  made 
very  light  and  small.  To  watch  the  movements  of  a  very 
small  needle  an  index  of  some  kind  must  be  used  ;  indeed,  in 
the  tangent  galvanometer  it  is  usual  to  fasten  to  the  short 
stout  needle  a  delicate  stiff  pointer  of  aluminium.  A  far 
better  method  is  to  fasten  to  the  needle  a  very  light  mirror 
of  silvered  glass,  by  means  of  which  a  beam  of  light  can  be 
reflected  on  to  a  scale,  so  that  every  slightest  motion  of  the 

1  Provided  the  current  is  not  too  strong ;    for  with  a  sine  galvanometer 
the  largest  current  which  can  be  measured  is  numerically  equal  to  H  -f-  G. 

2  Again  the  student  who  desires  to  compare  the  strength  of  two  currents 
will  require  the  help  of  a  table  of  natural  sines,  like  that  given  in  Appendix 
A.     Suppose  that  with  current  i  the  coils  had  to  be  turned  through  an 
angle  of  0  degrees ;    and  that  with  a  different  current  i'  the  coils  had  to  be 
turned  through  6'  degrees,  then 

i  :  i'  =  sin  6  :  sin  &'. 

It  is  of  course  assumed  that  the  instrument  is  provided  with  a  scale  of 
degrees  on  which  to  read  off  the  angle  through  which  the  coils  have  been 
turned.  It  is  possible  here  also,  for  rough  purposes,  to  graduate  the  circle 
not  in  degrees  of  arc,  but  in  portions  corresponding  to  equal  additional 
values  of  the  sine.  The  student  should  try  this  way  of  dividing  a  circle 
after  reading  the  note  on  "Ways  of  Reckoning  Angles,"  p.  127. 


198  ELECTRICITY  AND   MAGNETISM     [PT.  i.  228 

needle  is  magnified  and  made  apparent.  The  mirror  gal- 
vanometers devised  by  Sir  W.  Thomson  (Lord  Kelvin)  for 
signalling  through  submarine  cables  are  admirable  examples 
of  this  class  of  instrument.  In  Fig.  134  the  general  arrange- 
ments of  this  instrument  are  shown.  The  body  of  the  gal- 
vanometer, consisting  of  a  bobbin  on  which  is  wound  the  coil, 


FIG.  134.  —  Kelvin's  Mirror  Galvanometer. 

is  supported  on  three  screw  feet  by  which  it  can  be  adjusted. 
The  magnet  consists  of  one  or  more  small  pieces  of  steel  watch- 
spring  attached  to  the  back  of  a  light  concave  silvered  glass 
mirror  about  as  large  as  a  threepenny  piece,  weighing  alto- 
gether only  two  or  three  grains.  This  mirror  is  hung  by  a 
single  fibre  of  cocoon  silk  within  the  coil ;  and  a  curved  mag- 
net, which  serves  to  counteract  the  magnetism  of  the  earth, 
or  to  direct  the  needle,  is  carried  upon  a  vertical  support 
above.  Another  view  of  the  suspended  mirror  and  magnets 
is  shown  in  Fig.  135.  Opposite  the  galvanometer  is  placed 
the  scale.  A  beam  of  light  from  a  paraffin  lamp  passes 
through  a  narrow  aperture  under  the  scale  and  falls  on  the 
mirror,  which  reflects  it  back  on  to  the  scale.  The  mirror 
is  slightly  concave,  and  gives  a  well-defined  spot  of  light  if 


CH.  in.  229] 


MIRROR   GALVANOMETER 


199 


the  scale  is  adjusted  to  suit  the  focus  of  the  mirror.  The 
controlling  magnet  enables  the  operator  to  bring  the  reflected 
spot  of  light  to  the  zero  point  at  the  middle  of  the  scale. 
The  feeblest  current  passing 
through  the  galvanometer  will 
cause  the  spot  of  light  to  shift 
to  right  or  left.  The  tiny  cur- 
rent generated  by  dipping  into 
a  drop  of  salt  water  the  tip  of  a 
brass  pin  and  a  steel  needle 
(connected  by  wires  to  the  ter- 
FIO.  135.  —  Minor  minals  of  the  galvanometer) 


Galvanometer. 


FIG.  136.  —  Astatic 
Mirror  Galva- 
nometer. 


will  send  the  spot  of  light 
swinging  right  across  the  scale.  If  a  bright  beam  of  light  is 
used,  the  movement  of  the  needle  can  be  shown  to  a  thousand 
persons  at  once.  For  still  more  delicate  work  an  astatic 
pair  (Art.  214,  p.  180)  of  needles  can  be  used,  each  being 
surrounded  by  its  coil,  and  having  the  mirror  rigidly  attached 
to  one  of  the  needles.  Such  a  form,  with  two  bobbins,  wound 
so  as  to  be  traversed  by  the  current  in  opposite  senses,  is 
represented  diagrammatically  in  Fig.  136.  Such  an  instru- 
ment, made  with  four  bobbins,  two  in  front  and  two  behind 
the  suspended  needle  system,  and  having  on  each  bobbin 
about  2  miles  of  a  wire  about  yinnr  mcn  m  thickness,  insu- 
lated by  a  coating  of  silk,  is  capable  of  showing  by  a  deflexion 
of  one  millimeter  on  its  scale  an  exceedingly  minute  current, 
even  down  to  one  fifty-four  thousand  millionth  part  of  one 
ampere. 

229.  Suspended  Coil  Galvanometers.  —  These  have  been 
used  by  Sturgeon  (1836),  Varley  (1860),  and  others,  and  the 
principle  was  also  applied  in  Lord  Kelvin's  "  Siphon  Re- 
corder," Fig.  350.  The  best  known  is  that  of  d'Arsonval 
depicted  in  Fig.  137.  Between  the  poles  of  a  compound  per- 
manent steel  magnet  of  U-shape  is  suspended  by  very  thin 
hard-drawn  silver  wires  an  open  coil  of  very  fine  wire  wound 
on  a  light  rectangular  frame.  The  current  is  led  to  and 


200 


ELECTRICITY   AND   MAGNETISM      [PT.  i.  229 


mirror 


FIG.  137.  —  Suspended 
Coil  Galvanometer. 


from  the  coil  by  the  suspending  wires.  Within  the  suspended 
coil  is  a  cylinder  of  soft  iron,  supported  from  behind,  to 
concentrate  the  magnetic  field.  The  vertical  parts  of  the 
coil  then  hang  freely  in  the  two  narrow 
gaps  where  the  magnetic  field  is  very 
intense.  The  force  tending  to  turn  the 
coil  is  proportional  to  the  current,  to  the 
number  of  windings,  and  to  the  intensity 
of  the  magnetic  field,  so  that  by  making 
the  magnet  very  powerful  the  instrument 
becomes  very  sensitive.  The  elasticity  of 
the  suspending  wires  controls  the  position 
of  the  coil  and  tends  to  bring  it  back  to 
its  initial  position.  These  galvanometers 
are  independent  of  the  earth's  magnetic 
field,  and  are  not  affected  by  magnets  in 
their  neighbourhood,  so  that  they  can  be  used  in  many 
places  where  other  galvanometers  could  not. 
remarkably  dead-beat.  Some  are  provided 
with  a  pointer  and  a  horizontal  dial ;  others 
more  usually  have  a  mirror  attached  to 
the  coil  to  reflect  a  spot  of  light.  In  some 
the  moving  coil  is  supported  on  a  pivot, 
the  current  being  introduced  through  deli- 
cate flexible  springs. 

More  recent  is  the  suspended-coil  galva- 
nometer of  Ayrton  and  Mather  (Fig.  138). 
Here  the  suspended  coil  is  formed  as  an 
elongated  loop  with  no  wide  aperture  be- 
tween its  sides.  Consequently  the  poles 
of  the  magnets  may  be  brought  very  close 
together ;  and  these  are  made  up  of  a  num- 
ber  of  flat  steel  magnets  of  nearly  circular 
form  piled  up  on  one  another.  One  of  these  instruments 
with  mirror  and  scale,  at  a  standard  distance  of  one 
metre,  will  show  a  deflexion  of  one  millimetre  on  the  scale, 


They  are  also 


CH.  in.  230-232]    SENSITIVE    GALVANOMETER 


201 


with  a  current  less  than  one  ninety-millionth  part  of   one 
ampere. 

230.  Galvanometer  Shunts.  —  Strong  currents  must  not 
be  passed  through  very  sensitive  galvanometers,  for,   even 
if  they  are  not  spoiled  by  overheating,  the  deflexions  of  the 
needle  will  be  too  large  to  give  accurate  measurements.     In 
such  cases  the  galvanometer  is  used  with  a  shunt,  or  coil  of 
wire  arranged  so  that  the  greater  part  of  the  current  shall 
flow  through  it,  and  pass  by  the  galvanometer,  only  a  small 
portion  of  the  current  —  say  TV,  or  T£¥,  or  ToVo  —  actually 
traversing  the  coils  of  the  instrument.     The  resistance  of  the 
shunt  must  be  a  small  fraction  —  say  -J-,  or  -^ ,  or  ¥^¥  —  of 
the  resistance  of  the  instrument,  according  to  the  principle 
laid  down  in  Art.  441  about  branched  circuits. 

231.  Broca's    Galvanometer.  —  In    this    instrument    the 
special  astatic  combination  depicted  in  Fig.  124,  p.  182,  is 
used.     The  astatic  needles,  attached  to  a  mica  slip,  and 
hung  on  a  quartz  fibre, 

are  suspended  so  that 
the  central  poles  hang 
between  two  fixed 
coils.  A  deflexion  of 
one  millimetre  on  a 
scale  at  one  metre  dis- 
tance is  produced  by 
a  current  of  about  one 
thousand  millionth 
part  of  one  ampere. 

232.  String    Gal- 
vanometer. —  In   this 
instrument,    designed 
by  Einthoven  of  Ley- 
den,  the  moving  coil 

is  reduced  to  a  single  "  string"  or  fibre  of  silvered  glass, 
stretched  from  supports  along'a  narrow  gap  between  the  poles 
of  a  special  electromagnet .  As  the  ' '  string ' '  thus  lies  in  a  very 


FIG.  139.  —  String  Galvanometer. 


202  ELECTRICITY   AND   MAGNETISM     [PT.  i.  233-235 

strong  magnetic  field,  when  a  current  passes  through  it  it  is 
dragged  sideways  across  the  magnetic  lines  (see  Art.  367,  p. 
328),  and  its  deflexion,  which  is  proportional  to  the  current, 
is  observed  by  a  microscope  which  passes  through  a  hole 
bored  in  the  pole-pieces  (Fig.  139).  As  the  "  string"  weighs 

about gramme,  the  instrument  is  extraordinarily 

1,000,000 

sensitive,  as  well  as  dead-beat.  It  will  detect  a  current  less 
than  one  sixty-thousand  millionth  of  an  ampere. 

233.  Differential    Galvanometer.  —  For    the    purpose    of 
comparing  two  currents  a  galvanometer  is  sometimes  em- 
ployed, in  which  the  coil  consists  of  two  separate  wires  wound 
side  by  side.     If  two  equal  currents  are  sent  in  opposite 
directions  through  these  wires,  the  needle  will  not  move.     If 
the  currents  are  unequal,  then  the  needle  will  be  moved  with 
an  intensity  corresponding  to  the  difference  of  the  strengths 
of  the  two  currents. 

234.  Ballistic  Galvanometer.  —  In  order  to  measure  the 
strength   of   currents   which   last   only   a  very  short  time, 
galvanometers  are  employed  in  which  the  needle  takes  a 
relatively  long  time  to  swing.    This  is  the  case  with  long  or 
heavy  needles ;   or  the  needles  may  be  weighted  by  enclosing 
them  in  leaden  cases.     As  the  needle  swings  slowly  round, 
it  adds  up,  as  it  were,  the  varying  impulses  received  during 
the  passage  of  a  transient  current.     The  sine  of  half  the  angle 
of  the  first  swing  is  proportional  to  the  quantity  of  electricity 
that  has  flowed  through  the  coil.     The  charge  of  a  condenser 
may  thus  be  measured  by  discharging  it  through  a  ballistic 
galvanometer  (see  Art.  451  6).      The  needle  must  not  be 
damped. 

235.  Methods  of  Damping :    Aperiodic  Galvanometers.  — 
To   prevent   the   needle   from   swinging   to   and   fro   for   a 
long  time  devices  are  used  to  damp  the  motion.      These 
are:  — 

(a)  Air  Damping.  —  A  light  vane  attached  to  needle  beats 
against  the  air  and  damps  the  motion.     In  mirror  instruments 


CH.  in.  236]  OSCILLOGRAPHS  203 

the  mirror  itself  damps,  particularly  if  confined  in  a  narrow 
chamber. 

(6)  Oil  Damping.  —  A  vane  dips  into  oil. 

(c)  Magnetic  Damping.  —  If  the  needle  swings  close  to  or 
inside  a  mass  of  copper  or  aluminium,  it  will  soon  come  to 
rest  by  reason  of  the  eddy-currents  (Art.  500)  induced  in  the 
copper.  Eddy-currents  damp  the  motion  of  the  suspended 
coil  in  instruments  of  that  class,  particularly  if  the  coils  are 
wound  on  a  metal  frame. 

The  period  of  swing  can  be  reduced  by  diminishing  the 
weight  and  leverage  of  the  moving  parts  so  as  to  lessen 
their  moment  of  inertia.  It  can  also  be  lessened  (at  the 
expense  of  the  sensitiveness  of  the  instrument)  by  increas- 
ing the  controlling  forces.  An  instrument  so  well  damped 
as  to  come  to  rest  without  getting  up  a  periodic  swing  is 
called  an  aperiodic  or  dead-beat  instrument. 

236.    Oscillographs.  —  For   the   purpose   of   studying   ex- 
ceedingly rapid  changes  of   current,  or   rapidly  alternating 
currents,  instruments  called  oscillo- 
graphs have  been  devised  by  Blon- 
del  and  by  Duddell.     In  DuddelPs 
Oscillograph,  a  skeleton  diagram  of 
which  is  given  in  Fig.  140,  the  cur- 
rent is  sent  through  two  thin  parallel 
wires  forming  a  single  loop  stretched 
vertically  in  a  narrow  gap  between 
the  poles  of  an  excessively  strong 
electromagnet,  or  permanent  mag-         FIG.  140.  —  Duddeii's 
net.     The  loop  tends  to  turn  and 

moves  a  light  mirror.  The  movement  is  damped  by  immer- 
sion in  oil  of  the  lower  part  of  the  moving  system.  As  its 
moment  of  inertia  is  excessively  small  it  can  respond  to  cur- 
rents that  oscillate  with  a  frequency  of  several  hundreds  or 
even  thousands  per  second.  With  this  apparatus  it  is  usual 
to  combine  a  rotating  or  vibrating  mirror  for  the  study  of 
periodic  currents,  and  a  moving  photographic  plate  or  film 


204 


ELECTRICITY   AND   MAGNETISM       [PT.  i.  237 


to  record  the  deflexions  of  the  beam  of  light,  the  instanta- 
neous value  of  the  current  being  proportional  to  the  displace- 
ment of  the  luminous  spot. 

237.  Voltmeters,  or  Potential  Galvanometers.  —  If  any 
galvanometer  be  constructed  with  a  very  long  thin  wire  of 
high  resistance  as  its  coil,  or  included  in  the  circuit  of  its  coil, 
very  little  current  will  flow  through  it,  but  what  little  current 
flows  will  be  exactly  proportional  to  the  potential  difference 
that  may  be  applied  to  the  two  ends  of  its  circuit.  Such  a 

galvanometer,  suitably 
provided  with  a  scale, 
will  indicate  the  number 
of  volts  between  its  ter- 
minals. Many  forms 
of  voltmeter-galvanom- 
eters exist,  but  they 
all  agree  in  the  essential 
of  having  a  coil  or  cir- 
cuit of  a  high  resistance 
—  sometimes  several 
thousand  ohms.  The 
suspended-coil  galva- 
nometers described  in 
Art.  229,  with  an  auxil- 
iary high  resistance,  make  excellent  voltmeters.  Weston's 
voltmeter,  Fig.  141,  is  of  this  class,  the  coil  being  delicately 
pivoted,  and  controlled  by  a  spiral  spring.  Any  sensitive 
mirror  galvanometer  can  be  used  as  a  voltmeter  by  simply 
adding  externally  to  its  circuit  a  resistance  sufficiently  great. 
There  are  also  electrostatic  voltmeters  that  depend  on  the  repul- 
sion between  charged  surfaces  ;  they  are  a  species  of  electrom- 
eter and  are  described  in  Art.  309.  Hot-wire  voltmeters,  of 
which  Cardew's  (Art.  465,  p.  446)  was  the  earliest,  differ  from 
the  above  class  of  instrument.  The  essential  feature  of  these 
instruments  consists  in  a  long  thin  wire  of  high  resistance, 
which  expands  by  heating  when  it  is  connected  across  a  circuit. 


FIG.  141.  —  Weston's  Voltmeter. 


CH.  in.  238] 


AMPEREMETERS 


205 


All  voltmeters  are  placed  across  as  shunts  between  the  two 
points  the  potential  difference  of  which  is  to  be  measured. 
They  are  never  joined  up  in  circuit  as  amperemeters  are.  The 
range  of  a  voltmeter  may  be  increased  by  adding  resistance 
in  series  with  it. 

238.  Amperemeters,  or  Ammeters.  —  A  galvanometer 
graduated  so  that  its  index  reads  directly  on  the  scale  the 
number  of  amperes  (Art.  220)  flowing  through  the  coil  is 
called  an  Amperemeter.  Such  instruments  were  introduced 
in  form  for  industrial  use  in  1879  by  Ayrton  and  Perry. 
Amperemeters  are  made  with  short  coils  of  very  low  resist- 
ance and  few  turns  of  wire,  as  they  must  not  appreciably  add 
extra  resistance  to  the  circuit. 

Moving-coil  amperemeters  are  chiefly  used.  They  con- 
sist essentially  of  a  moving-coil  milli- voltmeter,  Fig.  141,  con- 
nected to  a  shunt  (Art.  230)  through  which  the  main  current 
passes.  As  the  fall  of  potential  across  the  shunt  is  propor- 
tional to  the  current  passing  through  it,  the  instrument 
scale  may  be  calibrated  to  read  direct 
in  amperes  for  that  particular  shunt. 

Among  the  innumerable  forms  of 
amperemeter  in  commerce  there  are  a 
number  in  which  there  is  neither  mag- 
net nor  iron,  but  which  depend  upon 
the  mutual  force  between  a  fixed  and 
a  movable  coil  traversed  by  the  cur- 
rent. These  are  dealt  with  in  Art. 
425,  and  are  suitable  for  alternate 
currents  as  well  as  continuous  currents.  Of  this  kind  are 
Siemens'  electrodynamometer  and  the  Kelvin  balances. 

Other  instruments  depend  upon  the  magnetic  properties 
of  iron  under  the  influence  of  the  current.  An  instrument  of 
the  moving-iron  type  is  depicted  in  Fig.  142.  It  consists  of  a 
coil  C  of  thick  wire  or  strip  with  a  narrow  rectangular  open- 
ing in  its  centre.  A  piece  of  soft  iron,  of  oval  shape  I  at- 
tached to  a  pointer,  is  pivoted,  so  that,  when  the  current 


142.  —  Moving 
Amperemeter. 


206  ELECTRICITY   AND   MAGNETISM   [PT.  i.  239,  240 

passes  around  the  coil,  the  iron  is  sucked  into  the  coil  by 
forces  depending  on  the  strength  of  the  current.  Gravity 
is  here  the  controlling  force. 

LESSON  XVIII.  —  Currents  produced  by  Induction 

239.  Faraday's  Discovery.  —  In  1831  Faraday  discovered 
that  currents  can  be  induced  in  a  closed  circuit  by  moving 
magnets  near  it,  or  by  moving  the  circuit  across  the  mag- 
netic field ;   and  he  followed  up  this  discovery  by  finding  that 
a  current  whose  strength  is  changing  may  induce  a  secondary 
current  in  a  closed  circuit  near  it.     Such  currents,  whether 
generated  by  magnets  or  by  other  currents,  are  known  as 
Induction  Currents.     And  the  action  of  a  magnet  or  current 
in   producing   such   induced   currents   is    termed   magneto- 
electric  (or  electromagnetic)  induction,1  or  simply  induction. 

Upon  this  principle  are  based  the  modern  dynamo  ma- 
chines for  generating  electric  currents  mechanically,  as  well 
as  induction  coils,  alternating-current  transformers,  and 
other  appliances. 

240.  Induction  of   Currents  by   Magnets.  —  If  a  coil  of 
insulated  wire  be  connected  in  circuit  with  a  sufficiently  deli- 
cate galvanometer,  and  a  magnet  be  inserted  rapidly  into  the 
hollow  of  the  coil  (as  in  Fig.  143),  a  momentary  current  is 
observed  to  flow  round  the  circuit  while  the  magnet  is  being 
moved  into  the  coil.     So  long  as  the  magnet  lies  motionless 
in  the  coil  it  induces  no  currents.     But  if  it  be  rapidly  pulled 
out  of  the  coil  another  momentary  current  will  be  observed 

1  The  student  must  not  confuse  this  electromagnetic  induction  with 
the  phenomenon  of  the  electrostatic  induction  of  one  charge  of  electricity 
by  another  charge,  as  explained  in  Lesson  III.,  and  which  has  nothing  to 
do  with  currents.  Formerly,  before  the  identity  of  the  electricity  derived 
from  different  sources  was  understood  (Art.  262),  electricity  derived  thus 
from  the  motion  of  magnets  was  termed  magneto-electricity.  For  most  pur- 
poses the  adjectives  magneto-electric  and  electro-magnetic  are  synonymous. 
The  production  of  electricity  from  magnetism,  and  of  magnetism  from 
electricity,  are,  it  is  true,  two  distinct  operations ;  but  both  are  included 
in  the  branch  of  science  denominated  Electromagnetics. 


CH.  m.  241]          INDUCTION   OF   CURRENTS  207 

to  flow,  and  in  the  opposite  direction  to  the  former.  The 
induced  current  caused  by  inserting  the  magnet  is  an  inverse 
current,  or  is  in  the  opposite  direction  to 
that  which  would  magnetize  the  magnet 
with  its  existing  polarity.  The  induced 
current  caused  by  withdrawing  the  mag- 
net is  a  direct  current. 

Precisely  the  same  effect  is  produced 
if  the  coil  be  moved  towards  the  magnet 
as  if  the  magnet  were  moved  towards  the 
coil.  The  more  rapid  the  motion  is,  the 
stronger  are  the  induced  currents.  FlG  143  __  Induction  of 

The  magnet  does  not  grow  any  weaker       Electric  current  by  a 

,        ,     .  j     .         .,  ,.          Magnet. 

by  being  so  used,  for  the  real  source  of 

the  electrical  energy  generated  is  the  mechanical  energy  spent 

in  the  motion. 

If  the  circuit  is  not  closed,  no  currents  are  produced ; 
but  the  relative  motion  of  coil  and  magnet  will  still  set  up 
electromotive  forces,  tending  to  produce  currents. 

Faraday  discovered  these  effects  to  be  connected  with  the 
magnetic  field  surrounding  the  magnet.  He  showed  that 
no  effect  was  produced  unless  the  circuit  cut  across  the  in- 
visible magnetic  lines  of  the  magnet. 

241.  Induction  of  Currents  by  Currents.  —  Faraday  also 
showed  that  the  approach  or  recession  of  a  current  might 
induce  a  current  in  a  closed  circuit  near  it.  This  may  be  con- 
veniently shown  as  an  experiment  by  the  apparatus  of  Fig. 
144. 

A  coil  of  insulated  wire  P  is  connected  in  circuit  with 
a  battery  B  of  two  or  three  cells,  and  a  key  K  to  turn  the 
current  on  or  off.  A  second  coil  S,  entirely  unconnected  with 
the  first,  is  joined  up  with  wires  to  a  sensitive  galvanometer 
G.  We  know  (Art.  215)  that  a  coil  of  wire  in  which  a  current 
is  circulating  acts  like  a  magnet.  And  we  find  that  if,  while 
the  current  is  flowing  in  P,  the  coil  is  suddenly  moved  up 
toward  S,  a  momentary  current  will  be  induced  in  S.  If  P 


208  ELECTRICITY   AND   MAGNETISM       [FT.  i.  241 

is  suddenly  moved  away  from  S  another  momentary  current 
will  be  observed  in  the  second  circuit.  The  first  of  these  two 
momentary  currents  is  an  "  inverse  "  one,  while  the  second 
one  is  found  to  be  a  "  direct  "  one  (i.e.  one  which  runs  the 
same  way  round  the  coil  S  as  the  battery  current  runs  round 
the  coil  P).  The  coil  P  is  called  the  primary  coil,  and  the 
current  in  it  the  primary  current.  The  other  coil  S  is  called 
the  secondary  coil,  and  the  momentary  currents  induced  in  it 
are  sometimes  called  secondary  currents. 

Let  P  now  be  placed  close  to  S,  no  current  flowing  in  either 
coil.     Then  on  pressing  the  key  K  to  switch  on  the  primary 


FIG.  144.  —  Induction  of  a  Current  by  a  Current. 

current,  it  will  be  noticed  that  during  the  moment  while  the 
current  in  P  is  growing  there  will  be  a  transient  inverse  cur- 
rent in  S.  The  effect  of  turning  on  the  current  is  just  as  if 
the  current  had  been  turned  on  while  P  was  far  away  and 
then  P  suddenly  brought  up  to  S.  Breaking  the  battery 
circuit  while  the  primary  coil  lies  close  to  the  secondary  coil 
produces  the  same  effect  as  if  the  primary  coil  were  suddenly 
removed  to  an  infinite  distance.  Making  the  battery  cir- 
cuit while  the  primary  coil  lies  close  to  the  secondary  pro- 
duces the  same  effect  as  bringing  it  up  suddenly  from  a  dis- 
tance. 

So  long  as  a  steady  current  traverses  the  primary  circuit 
there  are  no  induced  currents  in  the  secondary  circuit,  unless 
there  is  relative  motion  between  the  two  circuits  :  but  moving 


CH.  in.  242,  243]       LAWS   OF   INDUCTION 


209 


the  secondary  circuit  towards  the  primary  has  just  the  same 
effect  as  moving  the  primary  circuit  towards  the  secondary, 
and  vice  versa. 

We  may  tabulate  these  results  as  follows  :  — 


By 
means 
of 

Momentary  Inverse 
currents  are  induced 
in  the  secondary  circuit 

Momentary  Direct 
currents  are  induced 
in  the  secondary  circuit 

Magnet 

while  approaching. 

while  receding. 

Current 

while  approaching, 
or  beginning, 
or  increasing  in  strength. 

while  receding, 
or  ending, 
or  decreasing  in  strength. 

242.  Direction    of    Induced    E.M.F.  —  It    is    convenient 
to  have  rules  for  remembering  the  relations  in  direction  be- 
tween the  magnetism,  the  motion,  and  the  induced  electro- 
motive-force.    Of  such  rules  the  following,  due  to  Fleming,  is 
most  useful :     Let  the  forefinger  of  the  right  hand  (Fig.  145) 
point  in  the  direction  of  the  magnetic  lines;  then  turn  the  thumb 
in  the   direction   of   the  motion:    the 

middle  finger  bent  at  right  angles  to 
both  thumb  and  forefinger  will  show  the 
direction  of  the  induced  E.M.F. 

Another  rule  often  given  is  an 
adaptation  of  Ampere's :  Suppose  a 
figure  swimming  in  any  conductor  to 
turn  so  as  to  look  along  the  (positive 
direction  of  the}  lines,  then  if  he  and 
the  conductor  be  moved  towards  his  Fl°-  145>  —  Fleming's  Rule  of 

the  Right  Hand. 

right  hand  he  will  be  swimming  with 

the  current  induced  by  this  motion;    if  he  be  moved  towards 

his  left  hand,  the  current  will  be  against  him. 

243.  Fundamental  Laws  of  Induction.  —  When  we  reflect 
that  every  circuit  traversed  by  a  current  has  a  magnetic 
field  of  its  own  in  which  there  are  magnetic  lines  running 
through  the  circuit  (Arts.  215  and  420),  we  shall  see  that 

p 


210  ELECTRICITY   AND   MAGNETISM       [PT.  i.  243 

the  facts  tabulated  in  the  preceding  paragraph  may  be 
summed  up  in  the  following  fundamental  laws  :  — 

(i.)  A  decrease  in  the  number  of  lines  which  pass  through 
a  circuit  induces  a  current  round  the  circuit  in  the 
positive  direction  (i.e.  produces  a  <(  direct  "  current)  ; 
while  an  increase  in  the  number  of  lines  which  pass 
through  the  circuit  induces  a  current  in  the  negative 
direction  round  the  circuit  (i.e.  an  "  inverse  "  current). 

Here  we  suppose  the  positive  direction  along  lines  to  be 
the  direction  along  which  a  free  N-pole  would  tend  to  move, 
and  the  positive  direction  of  the  current  that  in  which  the 
current  must  flow  to  increase  the  magnetic  flux.  Compare 
the  "  corkscrew  "  rule  given  on  p.  178. 

(ii.)  The  total  induced  electromotive-force  acting  round  a 
closed  circuit  is  equal  to  the  rate  of  decrease  in  the 
number  of  lines  which  pass  through  the  circuit. 

Suppose  at  first  the  number  of  magnetic  lines  (Art.  121) 
passing  through  the  circuit  to  be  FI,  and  that  after  a  very 
short  interval  of  time  t  the  number  becomes  F2,  the  average 
induced  electromotive-force  E  is 

E  =  ~[~r 

By  Ohm's  law,  t  =  E  -f-  R, 

therefore  i  =  -^— ;  — 2. 

trt 

If  F2  is  greater  than  FI,  and  there  is  an  increase  in  the  number 
of  lines,  then  FI  —  F2  will  be  a  negative  quantity,  and  i  will 
have  a  negative  sign,  showing  that  the  E.M.F.  is  an  inverse 
one.  A  coil  of  50  turns  of  wire  cutting  1000  lines  will  produce 
the  same  effect  as  a  coil  of  5  turns  cutting  10,000  lines,  or  of 
one  turn  cutting  50,000  lines. 

To  induce  an  electromotive-force  equal  to  that  of  a  single 
Daniell's  cell  would  require  that  110,000,000  lines  should 
be  cut  in  one  second.  As  such  large  numbers  are  inconvenient 


Cj_|    I   I    I        ^— 


CH.  m.  243]  INDUCTIVE   OPERATIONS  211 

to  express  the  facts,  the  unit  of  E.M.F.,  the  volt,  has  been 
chosen  to  correspond  to  the  cutting  of  100,000,000  lines  per 
second.  » 

Example.  —  Suppose  the  number  of  magnetic  lines  to  diminish 
from  800,000  to  0  in  the  SV  of  a  second,  the  rate  of  diminu- 
tion is  40,000,000  lines  per  second.  And  since  1  volt  is 
taken  as  10 8  lines  per  second,  the  average  induced  E.M.F. 
during  that  time  will  be  0'4  volt. 

A  reference  to  Fig.  146  will  make  this  important  law 
clearer.  Suppose  ABCD  to  be  a  wire  circuit  of  which  the 
piece  AB  can  slide  along  DA  and  CB  towards  S  and  T. 
Let  the  vertical  arrows  represent  vertical  lines  of  force  in  a 
uniform  magnetic  field,  and  show  (as  is  the  case  with  the 
vertical  components  of  the 
earth's  lines  of  force  in  the 
northern  hemisphere)  the 
direction  in  which  a  N-  w 

pointing  pole  would  move 
if  free.  The  positive  direc- 
tion of  these  magnetic  lines  is  therefore  vertically  downwards 
through  the  circuit.  Now  if  AB  slide  towards  ST  with  a 
uniform  velocity  it  will  cut  a  certain  number  of  lines  every 
second,  and  a  certain  number  will  be  added  during  every 
second  of  time  to  the  total  number  passing  through  the 
circuit.  If  Fi  be  the  number  at  the  beginning,  and  F2  that 
at  the  end  of  a  circuit,  Fi  —  F2  will  be  a  negative  quantity, 
and  there  will  be  generated  an  electromotive-force  whose 
direction  through  the  sliding  piece  is  from  A  towards  B. 

The  electromotive-force  generated  is  directly  proportional 
to  the  strength  of  the  field  §,  to  the  velocity  v  of  the  move- 
ment, and  to  the  length  I  of  the  slider ;  or,  in  symbols : 

E  =  ©  X  /  X  v. 

Example.  —  Suppose  the  strength  of  the  field  to  be  §  =  6000 
lines  per  square  centimetre,  I  to  be  10  cm.,  and  v  to  be 
50  cm.  per  second ;  then  E,  which  is  the  rate  of  cutting  of 
magnetic  lines,  will  be  3,000,000  lines  per  second ;  or  (see 
Art.  381,  p.  342)  0'03  volt. 


212  ELECTRICITY   AND   MAGNETISM   [PT.  i.  244,  245 

It  is  important  to  note  that  all  these  inductive  opera- 
tions are  really  magnetic.  In  the  experiment  (Art.  241) 
with  the  two  coils  P  and  S  it  is  the  magnetic  lines  of  coil  P 
which  pass  through  coil  S  and  set  up  the  induced  E.M.F. 
This  is  proved  by  the  following  further  experiment.  Take  a 
bar  of  iron  —  a  poker,  or  better  still,  a  bundle  of  iron  wires  — 
and  lay  it  along  the  dotted  line  so  that  its  ends  pass  through 
P  and  S.  It  will  by  its  great  magnetic  permeability  help  to 
conduct  the  magnetic  lines  from  P  through  S.  And  when 
it  is  so  placed  it  will  be  found  greatly  to  intensify  the  actions. 
In  fact  if  P  is  many  inches  away  from  S,  and  the  iron  core  is 
present,  the  inductive  effects  of  turning  the  current  on  and 
off  may  be  as  great  as  if,  in  the  absence  of  the  core,  P  were 
pushed  up  close  to  S. 

244.  Faraday's    Disk    Machine.  —  Faraday    constructed 
several  magneto-electric  machines,  one  of  them  consisting 

of  a  copper  disk  (Fig.  147) 
which  he  rotated  between 
the  poles  of  a  steel  magnet  or 
electromagnet.  The  current 
flowed  from  shaft  to  rim,  or 
vice  versa,  according  to  the 
sense  of  the  rotation.  It  was 
conducted  away  by  wires  hav- 
ing sliding  contacts.  In  other 

FIG.   147.  —  Faraday's  Simple   Disk  Mag-    machines     Copper    wire     Coils 
neto-electric  Machine. 

were  spun  so  as  to  cut  mag- 
netic lines.  This  is  the  principle  applied  in  modern  dynamo- 
electric  machines  (Lesson  XLII).  In  all  cases  power,  whether 
of  arm  or  of  engine,  must  be  employed  to  produce  the  mo- 
tion. They  are  all  contrivances  for  converting  mechanical 
energy  into  electrical  energy. 

245.  Faraday's     Ring:    Principle    of    Transformation. — 
Amongst  Faraday's  earliest  experiments  he  took  an  iron 
ring  about  8  inches  in  diameter  (Fig.  148)  and  wound  upon  it 
two  insulated  coils  of  wire  P  and  S,  each  of  many  turns.    When 


CH.  in.  246] 


FARADAY'S   TRANSFORMER 


213 


coil  P  was  connected  to  a  battery  circuit,  and  coil  S  to  a  gal- 
vanometer, he  found  that  whenever  a  current  was  turned  on 
or  off  in  coil  P,  secondary  currents  were  generated  in  coil  S. 
In  fact  the  currents  in  P  magnetized  the  iron  ring,  and  the 
magnetic  lines  created  by  P  passed  through  S,  setting  up  in- 
duction currents.  If  S  is  used  as  the  primary  then  P  will 
work  as  secondary  ;  in  fact  the  induction  between  P  and  S  is 
mutual.  The  Faraday  ring,  with  its  two  coils  wound  upon  a 
closed  circuit  of  iron,  may  be  regarded  as  the  type  of  all  trans- 
formers or  induction  coils.  Faraday  also  employed  some  in- 
duction coils  in  which  the  two  coils  A  and  B  (Fig.  149)  were 


FIG.  148.  — -  Faraday's  Ring. 


FIG.    149.  —  Faraday's 
Transformer. 


wound  cylindrically  outside  one  another  upon  a  straight  core 
C  of  iron. 

In  all  transformers  the  electromotive-forces  generated  in 
the  secondary  circuit  are  to  those  employed  in  the  primary 
circuit,  nearly  in  the  same  proportion  as  the  relative  numbers 
of  turns  in  the  two  coils.  For  example,  if  the  primary  coil 
has  100  turns  and  the  secondary  has  2500  turns,  the  electro- 
motive-force in  the  secondary  circuit  will  be  nearly  twenty- 
five  times  as  great  as  that  used  in  the  primary.  By  choosing 
the  proper  number  of  turns,  the  electromotive-force  can  be 
transformed  either  up  or  down. 

246.  The  Induction  Coil.  —  In  order  to  generate  enor- 
mously high  electromotive-forces  which  shall  be  able  to 
send  sparks  across  air  spaces  that  ordinary  batteries  working 
at  less  than  100  volts  could  not  possibly  pierce,  advantage 
is  taken  of  the  transformer  principle.  To  produce  spark 


214  ELECTRICITY   AND   MAGNETISM      [PT.  i.  246 

discharges  there  is  used  the  apparatus  depicted  in  Fig. 
150,  as  improved  by  Callan,  Sturgeon,  Masson,  Ruhmkorff, 
Apps,  and  others,  and  termed  the  Induction  Coil  or  Induc- 
torium.  The  induction  coil  consists  of  a  cylindrical  bobbin 
having  a  central  iron  core  surrounded  by  a  short  inner  or 
"  primary  "  coil  of  stout  wire,  and  by  an  outer  "  secondary  " 
coil  consisting  of  many  thousand  turns  of  very  fine  wire, 
very  carefully  insulated  between  its  different  parts.  The 
primary  circuit  is  joined  to  the  terminals  of  a  few  cells, 
and  in  it  are  also  included  an  interrupter  (or  automatic 


FIG.  150.  —  Induction  Coil. 

break),  and  a  reversing  switch  or  key.  The  object  of  the 
interrupter  is  to  make  and  break  the  primary  circuit  in  rapid 
succession.  The  result  of  this  is  at  every  "  make  "  to  induce 
in  the  outer  "  secondary  "  circuit  a  momentary  inverse  elec- 
tromotive-force, and  at  every  "  break  "  a  powerful  moment- 
ary direct  electromotive-force.  As  the  number  of  magnetic 
lines  created  and  destroyed  at  each  "  make  "  and  "  break  " 
is  the  same,  the  two  electromotive  impulses  are  equal ;  but 
by  the  use  of  a  condenser  the  current  at  "  make  "  is  caused 
to  take  a  considerable  fraction  of  time  to  grow,  whilst  at 
"  break  "  the  cessation  is  instantaneous.  The  rate  of  cutting 


CH.  in.  247]  INDUCTION   COIL  215 

of  the  magnetic  lines  is  therefore  much  greater  at  "  break  " 
than  at  "  make."  The  induced  electromotive-forces  at 
"  make  "  last  longer,  but  are  feebler,  and  do  not  suffice  to 
send  sparks.  The  currents  at  "  break  "  manifest  themselves 
as  a  brilliant  torrent  of  sparks  between  the  ends  of  the 
secondary  wires  when  brought  near  enough  together.  The 
sparks  are  longer  and  only  pass  one  way,  but  they  differ 
merely  in  degree  from  those  furnished  by  friction  machines 
and  by  Ley  den  jars  (Arts.  330,  333).  For  studying  disrup- 
tive discharge  and  discharge  through  glass  vessels  and  tubes 
from  which  the  air  has  been  partially  exhausted  the  coil  is 
very  useful.  The  primary  coil  is  made  of  stout  wire,  that 
it  may  carry  strong  magnetizing  currents,  and  consists  of 
few  turns  to  keep  the  resistance  low,  and  to  avoid  self-induc- 
tion of  the  primary  current  on  itself.  The  central  iron  core 
is  for  the  purpose  of  increasing,  by  its  great  magnetic  per- 
meability, the  number  of  lines  of  force  that  pass  through 
the  coils :  it  is  usually  made  of  a  bundle  of  fine  wires  to 
avoid  the  induced  currents  which  if  it  were  a  solid  bar  would 
be  set  circulating  in  it,  and  which  would  retard  its  rapidity 
of  magnetization  or  demagnetization.  The  secondary  coil 
is  made  with  many  turns,  in  order  that  the  coefficient  of  trans- 
formation may  be  large ;  and  as  the  induced  electromotive- 
force  will  be  thousands  of  volts,  the  resistance  of  this  coil 
will  be  immaterial,  and  it  may  be  made  of  the  thinnest  wire 
that  can  conveniently  be  wound.  In  Mr.  Spottiswoode's 
giant  Induction  Coil  (which  yields  a  spark  of  42J  inches 
length  in  air,  when  worked  with  30  Grove's  cells),  the  sec- 
ondary coil  contains  280  miles  of  wire,  wound  in  340,000 
turns,  and  has  a  resistance  of  over  100,000  ohms. 

247.  Interrupters.  —  The  interrupters  of  induction  coils 
are  usually  self-acting.  That  of  Foucault,  shown  with  the 
coil  in  Fig.  150,  consists  of  an  arm  of  brass  L,  which  dips  a 
platinum  wire  into  a  cup  of  mercury  M,  from  which  it  draws 
the  point  out,  so  breaking  circuit,  in  consequence  of  its  other 
end  being  attracted  toward  the  core  of  the  coil  whenever 


216 


ELECTRICITY   AND   MAGNETISM      [PT.  i.  247 


it  is  magnetized  ;  the  arm  being  drawn  back  again  by  a  spring 
when,  on  the  breaking  of  the  circuit,  the  core  ceases  to  be  a 
magnet.  A  more  common  interrupter  on  small  coils  is  a 
"  break,"  consisting  of  a  piece  of  thin  steel  which  makes  con- 
tact with  a  platinum  point,  and  which  is  drawn  back  by  the 
attraction  of  the  core  on  the  passing  of  a  current ;  and  so 
makes  and  breaks  circuit  by  vibrating  backwards  and  forwards 

just  as  does  the  hammer  of  an 
ordinary  electric  bell. 

When  an  induction  coil  is  re- 
quired to  supply  an  X-ray  tube, 
a  switch  of  the  sprung  contact 
type  (Art.  207),  connected  in  the 
primary  circuit  and  rapidly  oper- 
ated by  hand,  will  act  as  a  suitable 
interrupter.  Rotary  breaks  or 
interrupters  are  largely  used  be- 
cause of  their  high  rate  of  inter- 
ruption and  the  regularity  of  the 
contact  periods.  A  small  cen- 
trifugal pump  p  suitably  rotated 
dips  in  mercury.  The  pump  sup- 
plies a  jet  j  with  mercury  which 
is  directed  on  to  a  contact  rod  opposite,  Fig.  151,  but  rotating 
on  the  same  shaft  as  the  pump  are  pointed  sectors  which  peri- 
odically intercept  the  jet  of  mercury  and  thus  break  contact. 
The  jet  can  be  raised  or  lowered  and  so  the  time  of  contact 
varied.  An  electrolytic  interrupter  devised  by  Wehnelt  con- 
sists of  two  electrodes  dipping  into  a  solution  of  sulphuric 
acid.  The  kathode  is  a  lead  plate,  and  the  anode  is  a  plati- 
num point  on  which  bubbles  of  gas  form,  and  escape,  when  a 
current  is  supplied  to  it ;  and  so  the  current  is  broken  by  the 
bubbles  and  made  again  when  they  escape. 

Associated  with  the  primary  circuit  of  a  coil  is  usually  a 
small  condenser  (see  Art.  322),  made  of  alternate  layers  of 
tinfoil  and  paraffined  paper,  into  which  the  current  flows 


FIG.  151.  —  Mercury  Break  or 
Interrupter. 


CH.  in.  248,  249]   RUHMKORFF'S   REVERSER 


217 


whenever  circuit  is  broken.  The  effect  of  the  condenser  is, 
as  stated  above,  to  suppress  the  "  inverse "  current  at 
"  make  "  and  to  increase  greatly  the  "  direct  "  electromotive- 
force  at  "  break."  The  condenser  does  this  by  the  action 
known  as  electric  resonance  (see  Art.  529).  The  sparks  are 
longer,  and  only  pass  one  way. 

248.  Ruhmkorff's  Reverser.  —  In  order  to  cut  off  or  re- 
verse the  direction  of  the  battery  current  at  will,  Ruhmkorff 
applied  the  current-reverser,  or  re versing-s witch  ("  commu- 
tator ")  shown  in  Fig.  152.     In  this  instrument  the  battery 
poles  are  connected 

through  the  ends  of 

the  axis  of  a  small 

ivory     or     ebonite 

cylinder     to      two 

cheeks   of  brass  V 

and  V,  which  can 

be  turned  so  as  to 

place   them    either 

way  in  contact  with 

two  vertical  springs 

B  and  C,  which  are 

joined  to  the  ends 

of  the  primary  coil. 

Many  other  forms  of  reversing-switch  have  been  devised ; 

one,  much  used  as  a  key  for  telegraphic  signalling,  is  drawn 

in  Fig.  343. 

249.  Induction   Currents  from  Earth's   Magnetism,  —  It 
is  easy  to  obtain  induced  currents  from  the  earth's  magnetism. 
A  coil  of  fine  wire  joined  to  a  sensitive  galvanometer,  when 
suddenly  inverted,  cuts  the  lines  of  the  earth's  magnetism, 
and  induces  a  current. 

Faraday,  indeed,  applied  this  method  to  investigate  the 
direction  and  number  of  magnetic  lines.  If  a  small  wire 
coil  be  joined  in  circuit  with  a  suitable  galvanometer  having 
a  heavy  needle,  and  the  little  coil  be  suddenly  inverted  while 


FIG.  152.  —  Ruhmkorff's  Reverser. 


218  ELECTRICITY   AND   MAGNETISM    [PT.  i.  250,  251 

in  a  magnetic  field,  it  will  cut  twice  all  the  lines  that  pass 
through  its  own  area,  and  the  sine  of  half  the  angle  of  the  first 
swing  (Art.  451)  will  be  proportional  to  the  number  of  lines 
cut ;  for  with  a  slow-moving  needle  the  total  quantity  of  elec- 
tricity that  flows  through  the  coils  will  be  the  integral  whole 
of  all  the  separate  quantities  conveyed  by  the  induced  cur- 
rents, strong  or  weak,  which  flow  round  the  circuit  during 
the  rapid  process  of  cutting  the  lines.  The  little  exploring 
coil  acts  therefore  as  a  magnetic  proof -plane.  For  small  de- 
flexions the  first  swing  may  be  taken  as  a  sufficient  approxi- 
mation instead  of  the  sine  of  half  the  angle  (see  Art.  234). 

If  the  circuit  be  moved  parallel  to  itself  across  a  uniform 
magnetic  field  there  will  be  no  induction  currents,  for  just  as 
many  magnetic  lines  will  be  cut  in  moving  ahead  in  front 
as  are  left  behind.  There  will  be  no  current  in  a  wire  moved 
parallel  to  itself  along  a  line  of  force ;  nor,  if  it  lie  along  such  a 
line  while  a  current  is  sent  through  it,  will  it  experience  any 
mechanical  force. 


LESSON  XIX.  —  Chemical  Actions  of  Currents 

250.  Conducting  Properties  of  Liquids.  —  In  addition  to 
the  chemical  actions  inside  the  cells  of  the  battery,  which 
always  accompany  the  production  of  a  current,  there  are  also 
chemical  actions  produced  outside  the  battery  when  the 
current  is  caused  to  pass  through  certain  liquids.     Liquids 
may  be  divided  into  three  classes  —  (1)  those  which  do  not 
conduct  at  all,  such  as  turpentine  and  many  oils,  particularly 
petroleum;     (2)  those  which  conduct  without  decomposition, 
viz.  mercury  and  other  molten  metals,  which  conduct  just  as 
solid  metals  do;     (3)  those  which  are  decomposed  when  they 
conduct  a  current,  viz.  the  dilute  acids,  solutions  of  metallic 
salts,  and  certain  fused  solid  compounds. 

251.  Decomposition  of  Water.  —  In  the  year   1800  Car- 
lisle and  Nicholson  discovered  that  the  voltaic  current  could 
be  passed  through  water,  and  that  in  passing  through  it  de- 


CH.  in.  252,  253]   ELECTROLYSIS   OF   WATER  219 

composed  a  portion  of  the  liquid  into  its  constituent  gases. 
These  gases  appeared  in  bubbles  on  the  ends  of  the  wires 
which  led  the  current  into  and  out  of  the  liquid ;  bubbles 
of  oxygen  gas  appearing  at  the  place  where  the  current  entered 
the  liquid,  and  hydrogen  bubbles  where  it  left  the  liquid.  It 
was  soon  found  that  a  great  many  other  liquids,  particularly 
dilute  acids  and  solutions  of  metallic  salts,  could  be  similarly 
decomposed  by  passing  a  current  through  them. 

252.  Electrolysis.  —  To   this   process   of   decomposing   a 
liquid  by  means  of  an  electric  current  Faraday  gave  the  name 
of  electrolysis  (i.e.  electric  analysis) ;    and  those  substances 
which  are  capable  of  being  thus  decomposed  or  "  electrolyzed" 
he  termed  electrolytes. 

The  ends  of  the  wires  leading  from  and  to  the  battery 
are  called  electrodes ;  and  to  distinguish  them,  that  by 
which  the  current  enters  is  called  the  anode,  that  by  which 
it  leaves  the  kathode.  The  vessel  in  which  a  liquid  is  placed 
for  electrolysis  is  termed  an  electrolytic  cell. 

253.  Electrolysis  of  Water.  —  Returning  to  the  decomposi- 
tion of  water,  we  may  remark  that  perfectly  pure  water  ap- 
pears not  to  conduct,  but  its  resistance  is  greatly  reduced  by 
the  addition  of  a  few  drops  of  sulphuric  or  hydrochloric  acid. 
The  apparatus  shown  in  Fig.  153  is  suitable  for  this  purpose. 
Here  a  battery  of  two  cells  (those  shown  are  circular  Bunsen's 
cells)  is  seen  with  its  poles  connected  to  two  strips  of  metallic 
platinum  as  electrodes,  which  project  up  into  a  vessel  con- 
taining the  acidulated  water.     Two  tubes  closed  at  one  end, 
which  have  been  previously  filled  with  water  and  inverted, 
receive  the  gases  evolved  at  the  electrodes.     Platinum  is  pre- 
ferred to  other  metals  such  as  copper  or  iron  for  electrodes, 
since  it  is  less  oxidizable  and  resists  every  acid.     It  is  found 
that  there  is  almost  exactly  twice  as  much  hydrogen  gas  (by 
volume)  evolved  at  the  kathode  as  there  is  of  oxygen  at  the 
anode.     This   fact   corresponds   with   the   known   chemical 
composition    of    water,   which   is   produced    by   combining 
together  these  two  gases  in  the  proportion  of  two  volumes  of 


220 


ELECTRICITY   AND   MAGNETISM      [PT.  i.  254 


the  former  to  one  of  the  latter.  The  proportions  of  gases 
evolved,  however,  are  not  exactly  two  to  one,  for  at  first  a 
very  small  quantity  of  the  hydrogen  is  absorbed  or  "  oc- 
cluded "  by  the  platinum  surface,  while  a  more  considerable 
proportion  of  the  oxygen  —  about  1  per  cent  —  is  given  off 
in  the  denser  allotropic  form  of  ozone,  which  occupies  less 
space  and  is  also  slightly  soluble  in  the  water.  When  a 
sufficient  amount  of  the  gases  has  been  evolved  and  collected 
they  may  be  tested ;  the  hydrogen  by  showing  that  it  will 


FIG.  153.  —  Water  Voltameter. 

burn,  the  oxygen  by  its  causing  a  glowing  spark  on  the  end  of 
a  splinter  of  wood  to  burst  into  flame.  If  the  two  gases  are 
collected  together  in  a  common  receiver,  the  mixed  gas  will 
be  found  to  possess  the  well-known  explosive  property  of 
mixed  hydrogen  and  oxygen  gases.  The  chemical  decompo- 
sition is  expressed  in  the  following  equation : 

H20  H2  +  O 

water       yields       2  vols.  of  Hydrogen         and        1  vol.  of  Oxygen 

254.  Electrolysis  of  Sulphate  of  Copper.  —  We  will  take 
as  another  case  the  electrolysis  of  a  solution  of  the  well- 
known  "  blue  vitriol  "  or  sulphate  of  copper.  If  a  few  crys- 
tals of  this  substance  are  dissolved  in  water  a  blue  liquid  is 


CH.  in.  255]  ANIONS   AND    KATIONS  221 

obtained,  which  is  easily  electrolyzed  between  two  electrodes 
of  platinum  foil,  by  the  current  from  a  single  cell  of  any  ordi- 
nary battery.  The  chemical  formula  for  sulphate  of  copper 
is  CuS04.  The  result  of  the  electrolysis  is  to  split  it  up  in 
two  parts.  Metallic  copper  is  carried  forward  by  the  current 
and  deposited  in  a  film  upon  the  kathode,  leaving  behind  at 
the  anode  "  sulphion,"  an  easily  decomposed  compound  of 
sulphur  and  oxygen,  which  is  immediately  acted  upon  by  the 
water,  forming  sulphuric  acid  and  oxygen.  This  oxygen  is 
liberated  in  bubbles  at  the  anode.  The  chemical  changes  are 
thus  expressed : 

CuSO4  Cu         +  SO4 

Sulphate  of  Copper  becomes    Copper        and          Sulphion ; 

SO4        +        H20  H2SO4        +        O 

Sulphion       and          water          produce    Sulphuric  acid    and    Oxygen. 

In  this  way,  as  the  current  continues  to  flow,  copper 
is  continually  withdrawn  from  the  liquid  and  deposited  on 
the  kathode,  and  the  liquid  gets  more  and  more  acid.  If 
copper  electrodes  are  used,  instead  of  platinum,  no  oxygen 
is  given  off  at  the  anode,  but  the  copper  anode  itself  dissolves 
away  into  the  liquid  at  exactly  the  same  rate  as  the  copper 
of  the  liquid  is  deposited  on  the  kathode. 

255.  Anions  and  Kations.  —  The  atoms  which  thus  are 
severed  from  one  another  and  carried  invisibly  by  the  current 
to  the  electrodes,  and  there  deposited,  are  obviously  of  two 
classes ;  some  are  carried  backward  or  left  behind  at  the  anode, 
others  are  carried  forward  to  the  kathode.  Faraday  gave  the 
name  of  ions  1  to  these  wandering  atoms  or  groups  of  atoms ; 

1  The  term  ions,  as  introduced  by  Faraday,  was  used  by  him  in  a  wider 
sense  than  that  adopted  to-day  by  most  electrochemists,  to  denote  not 
only  the  single  electrically  charged  atoms  or  groups  of  atoms,  but  also  the 
substances  so  acting.  In  Art.  824  of  his  Experimental  Researches  he  wrote : 
"Then,  again,  the  substances  into  which  these  [the  decomposable  sub- 
stances or  electrolytes]  divide,  under  the  influence  of  the  electric  current 
form  an  exceedingly  important  general  class.  ...  I  have  proposed  to  call 
these  bodies  generally  ions,  or  particularly  anions  and  cations,  according 
as  they  appear  at  the  anode  or  cathode;  and  the  numbers  representing  the 


222  ELECTRICITY   AND   MAGNETISM      [PT.  i.  256 

those  going  to  the  anode  being  anions,  and  those  going  to  the 
kathode  being  kations.  Anions  are  sometimes  regarded  as 
"  electronegative,"  because  they  move" as  if  attracted  toward 
the  +  pole  of  the  battery,  while  the  kations  are  regarded  as 
"  electropositive."  Hydrogen  and  the  metals  are  kations, 
moving  apparently  with  the  direction  assumed  as  that  of  the 
current,  and  are  deposited  where  the  current  leaves  the  elec- 
trolytic cell.  The  anions  are  oxygen,  chlorine,  etc.  When, 
for  example,  chloride  of  tin  is  electrolyzed,  metallic  tin  is 
deposited  on  the  kathode,  and  chlorine  gas  is  evolved  at  the 
anode. 

256.    Quantitative  Laws  of  Electrolysis. 

(i.)  The  amount  of  chemical  action  is  equal  at  all  points  of 
a  circuit.  If  two  or  more  electrolytic  cells  are  placed  at  dif- 
ferent points  of  a  simple  circuit  the  amount  of  chemical  ac- 
tion will  be  the  same  in  all,  for  the  same  quantity  of  electricity 
flows  past  every  point  of  the  circuit  in  the  same  time.  If  all 
these  cells  contain  acidulated  water,  the  quantity,  for  example 
of  hydrogen,  set  free  in  each  will  be  the  same ;  or,  if  they  con- 
tain a  solution  of  sulphate  of  copper,  identical  quantities  of 
copper  will  be  deposited  in  each.  If  some  of  the  cells  contain 
acidulated  water,  and  others  contain  sulphate  of  copper,  the 
weights  of  hydrogen  and  of  copper  will  not  be  equal,  but  will 
be  in  chemically  equivalent  quantities. 

(ii.)  The  amount  of  substance  liberated  at  an  electrode  in 
a  given  time  is  proportional  to  the  strength  of  the  current.  A 
current  of  two  amperes  will  cause  just  twice  the  quantity  of 
chemical  decomposition  to  take  place  as  a  current  of  one 
ampere  would  do  in  the  same  time. 

(iii.)   The  amount  of  substance  liberated  at  an  electrode  in 

proportions  in  which  they  are  evolved  electrochemical  equivalents.  Thus 
hydrogen,  oxygen,  chlorine,  iodine,  lead,  tin,  are  ions."  Or  again,  Art. 
829,  "A  body  decomposable  by  the  electric  current,  i.e.  an  electrolyte,  must 
consist  of  two  ions,  and  must  also  render  them  up  during  the  act  of  decom- 
position." Nowadays  electrochemists  do  not  call  the  substance  hydrogen 
an  ion :  they  would  say  one  atom  of  hydrogen  plus  its  atomic  charge  is  one 
hydrogen  ion. 


CH.  m.  256]    ELECTROCHEMICAL   EQUIVALENTS  223 

one  second  is  equal  to  the  strength  of  the  current  multiplied  by 
the  "  electrochemical  equivalent  "  of  that  substance.  It  has 
been  found  by  experiment  that  the  passage  of  one  coulomb 
of  electricity  through  a  solution  of  silver  nitrate  liberates 
0-0011183  gramme  of  silver.  Hence  a  current  of  i  amperes 
will  liberate  i  X  0-0011183  gramme  of  silver  per  second. 
The  number  0-0011183  is  called  the  electrochemical  equivalent 
of  silver.  The  "  electrochemical  equivalents  "  of  other  ele- 
ments can  be  easily  calculated  if  their  chemical  "  equivalent  " 
is  known.  Thus  the  chemical  "  equivalent  "  of  hydrogen  is 
1-008,  while  that  of  silver  is  107-88.  Hence  the  electro- 
chemical equivalent  of  hydrogen  will  be  0-0011183  X  1-008 
-7-  107-88  =  0-00001044.  Hence  to  liberate  1-008  grammes 
of  hydrogen,  or  107-88  grammes  of  silver,  or  the  correspond- 
ing gramme-equivalent  of  any  other  element1  will  require  the 
passage  of  96,550  coulombs.  This  number  is  sometimes 
called  "  the  Faraday  "  number. 

The  chemical  equivalent  must  not  be  confounded  with 
the  atomic  weight.  The  atomic  weight  of  copper  is  63-57, 
that  is  to  say,  its  atoms  are  63-57  times  as  heavy  as  atoms 
of  hydrogen.  But  in  chemical  combinations  one  atom 
of  copper  replaces,  or  is  "  worth/'  two  atoms  of  hydrogen; 
hence  the  weight  of  copper  equivalent  to  1  of  hydrogen  is 
63-57  -7-  2  =  31-78.  In  all  cases  the  chemical  "  equivalent  " 

.    ,,  , .     ,  atomic  weight      ^ 

is  the  quotient — j — •     The    following    table    gives 

full  statistical  information. 

1  Faraday's  remark  in  1833  (Experimental  Researches,  Art.  869)  was : 
"If  we  adopt  the  atomic  theory  or  phraseology,  then  the  atoms  of  bodies 
which  are  equivalents  to  each  other  in  their  ordinary  chemical  action,  have 
equal  quantities  of  electricity  naturally  associated  with  them."  Maxwell,  in 
1873  (in  his  Treatise  on  Electricity  and  Magnetism,  Art.  260),  wrote  :  —  "  We 
may  therefore  assume  that  the  number  of  molecules  in  an  electro-chemical 
equivalent  is  N,  a  number  unknown  at  present,  but  which  we  may  hereafter 
find  means  to  determine.  Each  molecule,  therefore,  on  being  liberated  from 
the  state  of  combination  parts  with  a  charge  whose  magnitude  is  1  +  N. 
.  .  .  This  definite  quantity  of  electricity  we  shall  call  the  molecular  charge. 
If  it  were  known  it  would  be  the  most  natural  unit  of  electricity. 


224 


ELECTRICITY  AND  MAGNETISM        [PT.  i.  257 


TABLE  OF  ELECTROCHEMICAL  EQUIVALENTS,  ETC. 


SUBSTANCE 

SYMBOL 

ATOMIC 
WEIGHT 

VAL- 
ENCY 

CHEMICAL 
EQUIVA- 
LENT 

ELECTROCHEM- 
ICAL EQUIVA- 
LENT 
(Grammes  per 
coulomb) 

Kathionic  — 
Hydrogen      .... 
Potassium      .... 
Sodium     
Gold     

H 
K 

Na 
Au 

1-008 
39'1 
23-0 
197*2 

1 

1 

1 

3 

1-008 
39-1 
23-0 
6573 

0-00001044 
0*00040527 
0-00023839 
Q'00068129 

Silver 

Ag 

107  '88 

1 

107"88 

0*0011183 

Copper  (Cupric)     .     . 
„        (Cuprous)  . 
Mercury  (Mercuric)     . 
,,          (Mercurous)  . 
Tin  (Stannic)     .     .     . 
„     (Stannous)  .     .     . 
Iron  (Ferric)      .     .     . 
,,      (Ferrous)    .     .     . 
Nickel       
Zinc 

Cu 
Cu" 
Hg 
Hg" 
Sn 
Sn" 
Fe 
Fe" 
Ni 
Zn 

63*57 
63-57 
200 
200 
119 
119 
55-85 
55-85 
58-68 
65*37 

2 
1 
2 
1 
4 
2 
3 
2 
2 
9 

3178 
63-57 
100 
200 
29-75 
59-5 
18-61 
27-92 
29-34 
32  '68 

0-00032945 
0-00065890 
0-0010365 
0*002073 
0-00030836 
0-00061672 
0*00019289 
0-00028934 
0-00030411 
0  '00033873 

Cadmium       .... 
Lead 

Cd 
Pb 

112-4 
207  "1 

2 

9 

56-2 
103-5 

0-00058251 
0*00107278 

Ammonium   .... 
Anionic  —          • 
Oxygen      
Chlorine 

NH4 

O 
Cl 

18-04 

16 
35  '46 

1 

2 
1 

18-04 

8 
35  '46 

0*00018698 

0*00008292 
0*00036754 

Iodine  
Bromine 

I 
Br 

126-92 
79'92 

1 
1 

126-92 
79'92 

0*00131552 
0*00082837 

Cyanogen       .... 
Hydroxyl  
Sulphion   

CN 
OH 
SO4 

26-01 
17-01 
96'07 

1 
1 

a 

26*01 
17-01 
48-03 

0*00026959 
0*00017631 
0*00049783 

All  atoms  that  are  imi-valent  carry  exactly  the  same 
minute  quantity  of  electricity :  all  atoms  that  are  divalent 
carry  exactly  twice  that  amount ;  all  trivalent  atoms  carry 
three  times  the  amount.  Hence  the  inference  that  electricity 
itself  exists  in  definite  atomic  quantities.  Every  atom  con- 
veys a  quantity  of  electricity  proportional  to  its  valency, 
not  to  its  weight. 

257.  Weight  of  Element  deposited.  —  The  following  equa- 
tion embodies  the  rule  for  finding  the  weight  of  any  given 


CH.  in.  258, 259]  VOLTAMETERS  225 

ion  disengaged  from  an  electrolytic  solution  during  a  known 
time  by  a  current  of  known  strength.  Let  i  be  the  current 
(reckoned  in  amperes),  t  the  time  (in  seconds),  z  the  electro- 
chemical equivalent,  and  w  the  weight  (in  grammes)  of  the 
element  liberated;  then 

w  =  zit, 

or,  in  words,  the  weight  (in  grammes)  of  an  element  deposited 
by  electrolysis  is  found  by  multiplying  its  electrochemical  equiva- 
lent by  the  strength  of  the  current  (in  amperes),  and  by  the 
time  (in  seconds)  during  which  the  current  continues  to  flow. 

Example.  —  A  current  from  five  Daniell's  cells  was  passed 
through  two  electrolytic  cells,  one  containing  a  solution 
of  silver,  the  other  acidulated  water,  for  ten  minutes. 
A  tangent  galvanometer  in  the  circuit  showed  the  strength 
of  the  current  to  be  0*5  amperes.  The  weight  of  silver 
deposited  will  be  0'0011183  X  0'5  X  10  X  60  =  0*3355 
gramme.  The  weight  of  hydrogen  evolved  in  the  sec- 
ond cell  will  be  0'00001044  X  0'5  X  10  X  60  =  0'003132 
gramme. 

258.  Voltameters.  —  The  second  of  the  above  laws,  that 
the  amount  of  substance  liberated  in  a  given  time  is  propor- 
tional to  the  current,  is  sometimes  known  as  Faraday's  Law, 
from  its  discoverer.     Faraday  pointed  out  that  it  affords  a 
chemical  means  of  measuring  currents.     He  gave  the  name 
of  voltameter  to  an  electrolytic  cell  arranged  for  the  purpose 
of  measuring  the  current  by  the  amount  of  chemical  action 
which  it  effects. 

259.  Water- Voltameter.  —  The  apparatus  shown  in  Fig. 
153   might  be   appropriately  termed  a  Water- Voltameter, 
provided  the  tubes  to  collect  the  gases  be  graduated,  so  as 
to  measure  the  quantities   evolved.     The  weight   of  each 
measured  cubic  centimetre  of  hydrogen   (at  the  standard 
temperature  of  0°  C.,  and  pressure  of  1  atmosphere)  is  known 
to  be  0-00008988  gramme.     Hence,  if  the  number  of  cubic 
centimetres  liberated  during  a  given  time  by  a  current  of 
unknown  strength  be  ascertained,  the  mean  strength  of  the 

Q 


226  ELECTRICITY  AND  MAGNETISM    [PT.  i.  260,  261 

current  can  be  calculated  by  first  reducing  the  volume  to 
weight,  and  then  dividing  by  the  electrochemical  equivalent, 
and  by  the  time.  Each  coulomb  of  electricity  liberates  in  its 
flow  0-1162  cubic  centimetre  of  hydrogen,  and  0-0581  c.c. 
of  oxygen.  If  these  gases  are  collected  together  in  a  mixed- 
gas  voltameter  there  will  be  0-1743  c.c.  of  the  mixed  gases 
evolved  for  every  coulomb  of  electricity  which  passes.  To 
decompose  9-008  grammes  of  water,  liberating  0-008  gramme 
of  H  and  8  grammes  of  0,  requires  96550  coulombs  to  be  sent 
through  the  liquid  with  an  electromotive  force  of  at  least 
1-47  volts  (see  Art.  566). 

260.  Copper    and    Silver    Voltameters.  —  As    mentioned 
above,  if  sulphate  of  copper  is  electrolyzed  between  two  elec- 
trodes of  copper,  the  anode  is  slowly  dissolved,   and  the 
kathode  receives  an  equal  quantity  of  copper  as  a  deposit 
on    its    surface.     One    coulomb    of    electricity    will    cause 
0-0003291   gramme  to  be  deposited;    and  to  deposit  one 
gramme  weight  requires  a  total  quantity  of  3038  coulombs 
to  flow  through  the  electrodes.     A  current  of  one  ampere 
deposits  in  one  hour  1-185  grammes  of  copper,  or  4-0259 
grammes  of  silver. 

By  weighing  one  of  the  electrodes  before  and  after  the 
passage  of  a  current,  the  gain  (or  loss)  will  be  proportional 
to  the  quantity  of  electricity  that  has  passed.  In  1879 
Edison  applied  this  method  for  measuring  the  quantity  of 
electricity  supplied  to  houses  for  electric  lights  in  them ;  a 
small  copper  voltameter  being  placed  in  a  branch  of  the  cir- 
cuit which  supplied  the  house,  to  serve  as  a  meter.  (For 
supply  meters  see  Art.  460,  p.  437.) 

261.  Comparison  of  Voltameters  with  Galvanometers.  — 
It  will  be  seen  that  both  Galvanometers  and  Voltameters  are 
intended  to  measure  the  strength  of  currents,  one  by  mag- 
netic, the  other  by  chemical  means.     Faraday  demonstrated 
that  the  magnetic  and  the  chemical  actions  of  a  current  are 
proportional  to  one  another.     In  Fig.  154  a  is  shown  a  cir- 
cuit that  is  branched  so  that  the  current  divides,  part  going 


CH.  in.  262]  VOLTAMETERS  227 

through  a  branch  of  small  resistance  r  and  part  through  a 
branch  of  larger  resistance  R.  The  current  will  divide,  the 
greater  part  going  by  the  path  of  lesser  resistance.  Three 
amperemeters  are  used.  It  will  be  found  that  the  number 
of  amperes  in  the  main  circuit  is  equal  to  the  sum  of  the 
amperes  in  the  two  branches.  In  Fig.  1546  the  three  ampere- 
meters have  been  replaced  by  three  copper  voltameters. 
The  weight  of  copper  deposited  in  the  voltameter  A  in  the 
main  circuit  will  be  found  to  be  equal  to  the  sum  of  the 
weights  deposited  in  B  and  C  in  the  two  branches.  A  gal- 
vanometer shows,  however,  the  strength  of  the  current  at 


any  moment,  and  its  variations  in  strength  from  one  moment 
to  another,  by  the  position  of  the  needle.  In  a  voltameter, 
a  varying  current  may  liberate  the  atoms  of  copper  or  the 
bubbles  of  gas  rapidly  at  one  moment,  and  slowly  the  next, 
but  all  the  varying  quantities  will  be  simply  added  together 
in  the  total  yield.  In  fact,  the  voltameter  gives  us  the 
"  time  integral  "  of  the  current.  It  tells  us  what  quantity  of 
electricity  has  flowed  through  it  during  the  experiment, 
rather  than  how  strong  the  current  was  at  any  one  moment. 

262.  Chemical  Test  for  Weak  Currents.  —  A  very  feeble 
current  suffices  to  produce  a  perceptible  amount  of  change 
in  certain  chemical  substances.  If  a  few  crystals  of  the  white 
salt  iodide  of  potassium  are  dissolved  in  water,  and  then  a 
little  starch  paste  is  added,  a  very  sensitive  electrolyte  is 
obtained,  which  turns  to  a  dark  blue  colour  at  the  anode 
when  a  very  weak  current  passes  through  it.  The  decom- 
position of  the  salt  liberates  iodine  at  the  anode,  which,  act- 
ing on  the  starch,  forms  a  coloured  compound.  White 


228  ELECTRICITY   AND   MAGNETISM    [PT.  i.  263,  264 

blotting-paper,  dipped  into  the  prepared  liquid,  and  then 
laid  on  the  kathode  and  touched  by  the  anode,  affords  a 
convenient  way  of  examining  the  discoloration  due  to  a 
current.  A  solution  of  ferrocyanide  of  potassium  affords 
when  using  an  anode  of  iron  the  well-known  tint  of  Prussian 
blue.  Bain  proposed  to  utilize  this  in  a  Chemical  Writing 
Telegraph,  the  short  and  long  currents  transmitted  along 
the  line  being  thus  recorded  in  blue  marks  on  a  strip  of  pre- 
pared paper,  drawn  along  by  clockwork  under  an  iron  stylus 
joined  to  the  positive  wire.  Faraday  showed  that  chemical 
discoloration  of  paper  moistened  with  starch  and  iodide  of 
potassium  was  produced  by  the  passage  of  electricity  from 
sources  of  all  different  kinds  —  frictional,  voltaic,  thermo- 
electric, and  magneto-electric,  —  even  by  that  evolved  by 
the  Torpedo  and  the  Gymnotus  (see  Art.  77).  In  fact,  he 
relied  on  this  chemical  test  as  one  proof  of  the  identity  of  the 
different  kinds  of  electricity. 

263.  Internal  and  External  Actions.  —  In  an  earlier  lesson 
it  was  shown  that  the  quantity  of  chemical  action  inside  the 
cells  of  the  battery  was  proportional  to  the  current.     Hence, 
Law  (i.)  of  Art.  256  applies  both  to  the  portion  of  the  circuit 
within  the  battery  and  to  that  without  it. 

Suppose  three  Daniell's  cells  are  being  employed  to  decompose 
water  in  a  voltameter.  Then  while  T008  gramme  weight  (11,620 
cub.  centims.)  of  hydrogen  and  8  grammes  (5810  c.c.)  of  oxygen 
are  set  free  in  the  voltameter,  31  '57  grammes  of  copper  will  be 
deposited  in  each  cell  of  the  battery,  and  (neglecting  loss  by  local 
action)  32*5  grammes  of  zinc  will  be  dissolved  in  each  cell. 

264.  Reversibility.  —  It  will  be  evident  that  the  electro- 
lytic cell  is  the  converse  of  the  voltaic  cell.     The  chemical 
work  done  in  the  voltaic  cell  furnishes  the  energy  of  the 
current  which  that  cell  sets  up  in  the  circuit.     In  the  elec- 
trolytic   cell    chemical    work   is    performed,    the   necessary 
energy  being  furnished  by  the  current  of  electricity  which 
is  sent  into  the  cell  from  an  independent  battery  or  other 
source.     It  is  important  to  note  the  bearing  of  this  with 


CH.  in.  265] 


REVERSIBILITY   OF   CELLS 


229 


respect  to  the  energy  of  the  circuit.  Suppose  a  current  of 
strength  i  to  flow  through  a  cell  of  which  the  electromotive- 
force  is  E,  and  which  acts  in  the  same  direction  as  the  current. 
The  energy  given  to  the  circuit  per  second  by  this  cell  will 
be  (Art.  454)  the  product  of  i  and  E;  the  chemical  energy 
of  the  voltaic  cell  entering  the  circuit  at  the  place  where  the 
chemical  action  is  going  on.  In  Fig.  155  the  current  is  in- 
dicated by  the  arrows  with  thick  shafts,  the  electromotive- 
force  by  the  feathered  arrow.  For  example,  if  10  amperes 
flow  through  a  Daniell  cell  acting  with  1-1  volts  of  electro- 
motive-force, the  power  given  out  by  the  cell  is  11  watts 
(Art.  454).  But  if  the  cell  be  so  connected  into  the  circuit, 
as  in  Case  II.  of  Fig.  155,  that  the 
E.M.F.  of  the  cell  opposes  the 
current  that  is  being  driven  along 
the  circuit,  then  the  energy  per 
second  will  be  the  product  of  i  and 
—  E,  or  —  -iE,  the  negative  sign 
indicating  that  the  circuit  is  los-  Case 
ing  energy,  part  of  its  energy  being 
absorbed  in  the  cell  in  doing  chemi- 
cal work.  If  the  current  is  sent 
backwards  through  a  Daniell  cell  the  chemical  processes  are 
reversed,  copper  is  dissolved  and  zinc  is  deposited.  But  all 
cells  are  not  reversible  in  their  chemical  action. 

The  modern  theory  of  electrolysis,  and  some  examples  of 
its  application,  are  given  in  Art.  567  on  Electrochemical 
Energy. 


ii. 


E MF  helps  current. 
Energy  enters  circuit' 


EMF   opposes  current. 
Energy  leaves  circuit. 


FIG.  155. 


LESSON   XX.  —  Physical   and   Physiological   Effects   of  the 

Current 

265.  Molecular  Actions.  —  Metal  conductors,  when  sub- 
jected to  the  prolonged  action  of  currents,  undergo  slow 
molecular  changes.  Wires  of  copper  and  brass  gradually 
become  brittle  under  its  influence.  During  the  passage  of 


230  ELECTRICITY   AND   MAGNETISM    [PT.  i.  266-269 

the  current  through  metallic  wires  their  cohesion  is  tem- 
porarily lessened,  and  there  also  appears  to  be  a  decrease  in 
their  coefficient  of  elasticity. 

266.  Electric  Osmose.  —  Porret  observed  that  if  a  strong 
current  is  led  into  certain  liquids,  as  if  to  electrolyze  them, 
a  porous  partition  being  placed  between  the  electrodes,  the 
current  mechanically  carries  part  of  the  liquid  through  the 
porous  diaphragm,  so  that  the  liquid  is  forced  up  to  a  higher 
level  on  one  side  than  on  the  other.     This  phenomenon, 
known  as  electric  osmose,  is  most  manifest  when  badly-con- 
ducting liquids,  such  as  alcohol  and  bisulphide  of  carbon, 
are  used.     The  transfer  through  the  diaphragm  takes  place 
in  the  direction  of  the  current ;   that  is  to  say,  the  liquid  is 
higher  about  the  kathode  than  round  the  anode. 

267.  Electric   Distillation.  —  Closely  connected  with  the 
preceding  phenomenon  is  that  of  the  electric  distillation  of 
liquids.     It  was  noticed  by  Beccaria  that  an  electrified  liquid 
evaporated  more  rapidly  than  one  not  electrified.     In  a  bent 
closed  tube,  containing  two  portions  of  liquid,  one  of  which 
is  made  highly  +  and  the  other  highly  — ,  the  liquid  passes 
over  from  +  to  — .     This  apparent  distillation  is  not  due  to 
difference  of  temperature,  nor  does  it  depend  on  the  extent 
of  surface  exposed,  but  is  effected  by  a  slow  creeping  of  the 
liquid  along  the  interior  surface  of  the  glass  tubes.     Bad 
conductors,  such  as  turpentine,  do  not  thus  pass  over. 

268.  Diaphragm  Currents.  —  Quincke  discovered  that  a 
current  is  set  up  in  a  liquid  when  it  is  forced  by  pressure 
through  a  porous  diaphragm.     This  phenomenon  is  the  con- 
verse of  electric   osmose.     The  E.M.F.  so  produced  varies 
with  the  pressure  and  with  the  nature  of  the  diaphragm. 
When  water  was  forced  at  a  pressure  of  one  atmosphere 
through  sulphur,  the  difference  of  potential  was  over  9  volts. 
With  diaphragms  of  porcelain  and  bladder  the  differences 
were  only  0-35  and  0-01  volt  respectively. 

269.  Electro-Capillary  Phenomena.  —  If  a  horizontal  glass 
tube,  turned  up  at  the  ends,  be  filled  with  dilute  acid,  and 


CH.  in.  270]    VARIOUS   EFFECTS   OF   CURRENTS  231 

a  single  drop  of  mercury  be  placed  at  about  the  middle  of 
the  tube,  the  passage  of  a  current  through  the  tube  will 
cause  the  drop  to  move  along  towards  the  negative  pole. 
The  electrification  of  a  surface  modifies  those  properties 
which,  like  surface-tension,  depend  on  the  condition  of  the 
surface.  A  charge  of  potential  at  the  boundary  surface 
between  two  liquids  alters  the  electrification;  and  thus  a 
movement  results  from  the  capillary  forces.  Lippmann, 
Dewar,  and  others  have  constructed  upon  this  principle 
capillary  electrometers,  in  which  the  pressure  of  a  column  of 
liquid  is  made  to  balance  the  electro-capillary  force  exerted 
at  the  surface  of  contact  of  mercury  and  dilute  acid,  the 
electro-capillary  force  being  nearly  proportional  to  the  elec- 
tromotive-force when  this  does  not  exceed  one  volt.  Fig. 
156  shows  the  capillary  electrometer  of  Dewar.  A  glass 
tube  rests  horizontally  between  two  glass  dishes  in  which 
holes  have  been  bored  to  receive  the  ends  of  the  tube.  It  is 
filled  with  mercury,  and  a  single  drop  of  dilute  acid  is  placed 
in  the  tube.  Platinum  wires  to  serve  as  electrodes  dip  into 
the  mercury  in  the  dishes.  An  E.M.F.  of  only  -gfa  volt 
suffices  to  produce  a  measurable  displacement  of  the  drop. 
The  direction  of  the  displacement  varies  with  that  of  the 
current. 

270.  Physiological  Actions.  —  Currents  of  electricity 
passed  through  the  limbs  affect  the  nerves  with  certain 
painful  sensations,  and  cause  the  muscles  to  undergo  invol- 
untary contractions.  The  sudden  rush  of  even  a  small 
charge  of  electricity  from  a  Leyden  jar  charged  to  a  high 
potential,  or  from  an  induction  coil  (see  Fig.  150),  gives  a 
sharp  and  painful  shock  to  the  system.  The  current  from  a 
few  strong  Grove's  cells,  conveyed  through  the  body  by 
grasping  the  terminals  with  moistened  hands,  gives  a  very 
different  kind  of  sensation,  not  at  all  agreeable,  of  a  prickling 
in  the  joints  of  the  arms  and  shoulders,  but  not  producing 
any  spasmodic  contractions,  except  it  be  in  nervous  or 
weakly  persons,  at  the  sudden  making  or  breaking  of  the 


232  ELECTRICITY   AND   MAGNETISM       [PT.  i.  270 

circuit.  The  difference  between  the  two  cases  lies  in  the 
fact  that  the  tissues  of  the  body  offer  a  very  considerable 
resistance,  and  that  the  difference  of  potential  in  the  former 
case  may  be  many  thousands  of  volts;  hence,  though  the 
actual  quantity  stored  up  in  the  Ley  den  jar  is  very  small, 
its  very  high  E.M.F.  enables  it  at  once  to  overcome  the  re- 
sistance. The  battery,  although  it  might,  when  working 
through  a  good  conductor,  afford  in  one  second  a  thousand 
times  as  much  electricity,  cannot,  when  working  through 


FIG.  156.  —  Capillary  Electrometer. 

the  high  resistance  of  the  body,  and  particularly  of  the  skin, 
transmit  more  than  a  small  fraction,  owing  to  its  limited 
E.M.F. 

After  the  discovery  of  the  shock  of  the  Leyden  jar  by 
Cunaeus  in  1745  many  experiments  were  tried.  Louis  XV. 
of  France  caused  an  electric  shock  from  a  battery  of  Leyden 
jars  to  be  administered  to  700  Carthusian  monks  joined 
hand  in  hand,  with  prodigious  effect.  Franklin  killed  a 
turkey  by  a  shock  from  a  Leyden  jar. 

In  1752  Sulzer  remarked  that  "  if  you  join  two  pieces  of 
lead  and  silver,  and  then  lay  them  upon  the  tongue,  you  will 
notice  a  certain  taste  resembling  that  of  green  vitriol,  while 
each  piece  apart  produces  no  such  sensation."  This  gal- 
vanic taste,  not  then  suspected  to  have  any  connexion  with 
electricity,  may  be  experienced  by  placing  a  silver  coin  on 
the  tongue  and  a  steel  pen  under  it,  the  edges  of  them  being 
then  brought  into  metallic  contact.  The  same  taste  is 
noticed  if  the  two  wires  from  the  poles  of  a  single  voltaic 
cell  are  placed  in  contact  with  the  tongue.  The  saliva  acts 
as  an  electrolyte. 


CH.  in.  271]          PHYSIOLOGICAL  EFFECTS  233 

Ritter  discovered  that  a  feeble  current  transmitted  through 
the  eyeball  produces  the  sensation  as  of  a  bright  flash  of 
light  by  its  sudden  stimulation  of  the  optic  nerve.  A  stronger 
current  flowing  between  the  forehead  and  the  hand  gave  a 
sensation  of  blue  and  green  colours.  Von  Helmholtz,  re- 
peating this  experiment,  observed  only  a  wild  rush  of  colour. 
Dr.  Hunter  saw  flashes  of  light  when  a  piece  of  metal  placed 
under  the  tongue  was  touched  against  another  which  touched 
the  moist  tissues  of  the  eye.  Volta  and  Ritter  heard  musical 
sounds  when  a  current  was  passed  through  the  ears ;  and 
Humboldt  found  a  sensation  to  be  produced  in  the  organs  of 
smell  when  a  current  was  passed  from  the  nostril  to  the  soft 
palate.  Each  of  the  specialized  senses  can  be  stimulated 
into  activity  by  the  current.  Man  possesses  no  specialized 
sense  for  the  perception  of  electrical  forces,  as  he  does  for 
light  and  for  sound ;  but  there  is  no  reason  for  denying  the 
possibility  that  some  of  the  lower  creatures  may  be  endowed 
with  a  special  electrical  sense. 

The  following  experiment  shows  the  effect  of  feeble  cur- 
rents on  cold-blooded  creatures.  If  a  copper  (or  silver) 
coin  be  laid  on  a  piece  of  sheet  zinc,  and  a  common  garden 
snail  be  set  to  crawl  over  the  zinc,  directly  it  comes  into 
contact  with  the  copper  it  will  suddenly  pull  in  its  horns, 
and  shrink  in  its  body.  If  it  is  set  to  crawl  over  two  copper 
wires,  which  are  then  placed  in  contact  with  a  feeble  voltaic 
cell,  it  immediately  announces  the  establishment  of  a  current 
by  a  similar  contraction. 

271.  Muscular  Contractions.  —  In  1678  Swammerdam 
showed  to  the  Grand  Duke  of  Tuscany  that  when  a  portion 
of  muscle  of  a  frog's  leg  hanging  by  a  thread  of  nerve  bound 
with  silver  wire  was  held  over  a  copper  support,  so  that 
both  nerve  and  wire  touched  the  copper,  the  muscle  imme- 
diately contracted.  More  than  a  century  later  Galvani's 
attention  was  drawn  to  the  subject  by  his  observation  of 
spasmodic  contractions  in  the  legs  of  freshly-killed  frogs 
under  the  influence  of  the  "  return-shock "  experienced 


234  ELECTRICITY  AND   MAGNETISM      [PT.  i.  271 

every  time  a  neighbouring  electric  machine  was  discharged. 
Unaware  of  Swammerdam's  experiment,  he  discovered  in 
1786  the  fact  (alluded  to  in  Art.  171  as  leading  ultimately 
to  the  discovery  of  the  Voltaic  Pile)  that  when  nerve  and 
muscle  touch  two  dissimilar  metals  in  contact  with  one  an- 
other a  contraction  of  the  muscle  takes  place.  The  limbs  of 
the  frog,  prepared  as  directed  by  Galvani,  are  shown  in  Fig. 
157.  After  the  animal  has  been  killed  the  hind  limbs  are 
detached  and  skinned ;  the  crural  nerves  and  their  attach- 
ments to  the  lumbar 
vertebrae  remaining. 
For  some  hours  after 
death  the  limbs  retain 
their  contractile  power. 
The  frog's  limbs  thus 
prepared  form  an  ex- 
cessively delicate  gal- 
vanoscope ;  with  them, 
for  example,  the  exces- 
sively delicate  induc- 
tion-currents of  the  tele- 
phone (Lesson  LVII.) 
can  be  shown,  though 
the  most  sensitive  gal- 
vanometers barely  de- 

FIG.  157.  —  Muscular  Contraction  of  Frog's  Leg.  . ,  /->•    i          • 

tect    them.       Galvani 

and  Aldini  proved  that  other  creatures  undergo  like  effects. 
With  a  pile  of  100  pairs  Aldini  experimented  on  newly 
killed  sheep,  oxen,  and  rabbits,  and  found  them  to  suffer 
spasmodic  muscular  contractions.  Humboldt  proved  the 
same  on  fishes ;  and  Zanotti,  by  sending  a  current  through 
a  newly-killed  grasshopper,  caused  it  to  emit  its  familiar 
chirp.  Aldini,  and  later  Dr.  Ure  of  Glasgow,  experi- 
mented on  the  bodies  of  executed  criminals,  with  a  success 
terrible  to  behold.  The  facial  muscles  underwent  horrible 
contortions,  and  the  chest  heaved  with  the  contraction  of 


CH.  in.  272]        MUSCULAR   CONTRACTIONS  235 

the  diaphragm.  The  small  muscles  attached  to  the  roots 
of  the  hairs  of  the  head  appear  to  be  markedly  sensitive  to 
electrical  conditions  from  the  readiness  with  which  electri- 
fication causes  the  hair  to  stand  on  end. 

The  resistance  of  the  human  body  to  the  flow  of  electric 
current  through  it  depends  mainly  on  the  dryness  of  the  skin. 
It  may  vary  from  10,000  down  to  300  ohms  when  the  skin  is 
moist.  From  experiments  made  in  America  in  connexion 
with  the  execution  of  criminals,  it  was  found  that  the  aver- 
age resistance  of  the  human  body  is  2500  ohms,  and  that 
3000  (alternating)  volts  applied  between  the  head  and  spine 
caused  instantaneous  death. 

A  current  of  as  much  as  20  milliamperes  produces  terrible 
muscular  contractions,  whilst  a  current  of  2  amperes  trav- 
ersing a  vital  part  is  almost  certainly  fatal.  The  effect  of 
the  current  is  two-fold ;  in  the  first  place  it  acts  upon  the 
nerves,  causing  spasms,  secondly  it  destroys  the  tissue  either 
by  burning  or  by  electrolysis,  the  blood  becoming  coagulated. 
To  restore  a  person  who  has  been  rendered  insensible  by  an 
electric  shock,  all  the  same  restoratives  should  be  used  as 
for  a  person  drowned.  India-rubber  gloves  are  worn  by 
switch-board  operators,  as  a  protection,  in  high  voltage 
stations. 

272.  Conditions  of  Muscular  Contraction.  —  To  produce 
muscular  contraction  the  current  must  traverse  a  portion  of 
the  nerve  longitudinally.  In  a  freshly-prepared  frog  the 
current  causes  a  contraction  only  momentarily  when  the 
circuit  is  made  or  broken.  A  rapidly  interrupted  current 
will  induce  a  second  contraction  before  the  first  has  had 
time  to  pass  off,  and  the  muscle  may  exhibit  thus  a  con- 
tinuous contraction  resembling  tetanus.  The  prepared  frog 
after  a  short  time  becomes  less  sensitive,  and  a  "  direct  " 
current  (that  is  to  say,  one  passing  along  the  nerve  in  the 
direction  from  the  brain  to  the  muscle)  only  produces  an 
effect  when  circuit  is  made,  while  an  "  inverse  "  current 
only  produces  an  effect  when  the  circuit  is  broken.  Mat- 


236  ELECTRICITY   AND   MAGNETISM       [PT.  i.  273 

teucci,  who  observed  this,  also  discovered  by  experiments 
on  living  animals  that  there  is  a  distinction  between  the  con- 
ductivity of  sensory  and  motor  nerves,  —  a  "  direct  "  cur- 
rent affecting  the  motor  nerves  on  making  the  circuit,  and 
the  sensory  nerves  on  breaking  it ;  while  an  "  inverse  " 
current  produced  inverse  results.  Little  is,  however,  yet 
known  of  the  conditions  of  conductivity  of  the  matter  of 
the  nerves ;  they  conduct  better  than  muscular  tissue,  car- 
tilage, or  bone ;  but  of  all  substances  in  the  body  the  blood 
conducts  best.  Powerful  currents  doubtless  electrolyze  the 
blood  to  some  extent,  coagulating  it  and  the  albumin  it  con- 
tains. The  power  of  contracting  under  the  influence  of  the 
current  appears  to  be  a  distinguishing  property  of  proto- 
plasm wherever  it  occurs.  The  amoeba,  the  most  structure- 
less of  organisms,  suffers  .contractions.  Ritter  discovered 
that  the  sensitive  plant  shuts  up  when  electrified,  and  Burdon 
Sanderson  showed  that  this  property  extends  to  other  vege- 
tables, being  exhibited  by  the  carnivorous  plant,  the  Dionaea 
or  Venus's  Fly  Trap. 

273.  Animal  Electricity.  —  Although,  in  his  later  writings 
at  least,  Galvani  admitted  that  the  electricity  thus  operating 
arose  from  the  metals  employed,  he  insisted  on  the  existence 
of  an  animal  electricity  resident  in  the  muscular  and  nervous 
structures.  He  showed  that  contractions  could  be  produced 
without  using  any  metals  at  all  by  merely  touching  a  nerve 
at  two  different  points  along  its  length  with  a  morsel  of 
muscle  cut  from  a  living  frog ;  and  that  a  conductor  of  one 
metal  when  joining  a  nerve  to  a  muscle  also  sufficed  to 
cause  contraction  in  the  latter.  Galvani  and  Aldini  regarded 
these  facts  as  a  disproof  of  Volta's  contact-theory.  Volta 
regarded  them  as  proving  that  the  contact  between  nerve 
and  muscle  itself  produced  (as  in  the  case  of  two  dissimilar 
metals)  opposite  electrical  conditions.  Nobili,  later,  showed 
that  when  the  nerve  and  the  muscle  of  the  frog  are  respectively 
connected  by  a  water-contact  with  the  terminals  of  a  deli- 
cate galvanometer,  a  current  is  produced  which  lasts  several 


CH.  in.  274]  ANIMAL  ELECTRICITY  237 

hours :  he  even  arranged  a  number  of  frogs'  legs  in  series, 
like  the  cells  of  a  battery,  and  thus  increased  the  current. 
Matteucci  showed  that  through  the  muscle  alone  there  may 
be  an  electromotive-force.  Du  Bois  Reymond  has  shown 
that  if  the  end  of  a  muscle  be  cut  across,  the  ends  of  the  mus- 
cular fibres  of  the  transverse  section  are  negative,  and  the 
sides  of  the  muscular  fibres  are  positive,  and  that  this  differ- 
ence of  potential  will  produce  a  current  even  while  the  muscle 
is  at  rest.  To  demonstrate  this  he  employed  a  fine  astatic 
galvanometer  with  20,000  turns  of  wire  in  its  coils ;  and  to 
obviate  errors  arising  from  the  contact  of  the  ends  of  the 
wires  with  the  tissues,  unpolarizable  electrodes  were  used, 
made  by  plunging  terminal  zinc  points  into  a  saturated  solu- 
tion of  sulphate  of  zinc,  contained  in  a  fine  glass  tube,  the 
end  of  which  was  stopped  with  a  porous  plug  of  moistened 
china  clay.  Normal  muscle  at  rest  shows  no  current  what- 
ever between  its  parts.  Injured  muscle  at  rest  shows  a 
current  from  the  injured  toward  the  uninjured  part  (return- 
ing toward  the  injured  part  through  the  galvanometer). 
Normal  muscle  when  active  shows  a  current  from  the  active 
part  toward  the  resting  part.  Du  Bois  Reymond  obtained 
currents  from  his  own  muscles  by  dipping  the  tips  of  his 
fore-fingers  into  two  cups  of  salt  water  communicating  with 
the  galvanometer  terminals.  A  sudden  contraction  of  the 
muscles  of  either  arm  produced  a  current  from  the  con- 
tracted toward  the  uncontracted  muscles.  Dewar  has  shown 
that  when  light  falls  upon  the  retina  of  the  eye  an  electric 
current  is  set  up  in  the  optic  nerve.  Waller  has  investi- 
gated the  electromotive-forces  set  up  by  the  beating  of  the 
heart.  These  are  best  observed  by  using  a  string  galva- 
nometer (Art.  232)  with  photographic  registration.  In  the 
skin,  and  especially  in  the  skin  of  the  common  eel,  there  is 
an  electromotive-force  from  without  inwards. 

274.  Surgical  Applications.  —  Electric  currents  have  been 
successively  employed  as  an  adjunct  in  restoring  persons 
rescued  from  drowning;  the  contraction  of  the  diaphragm 


238  ELECTRICITY   AND   MAGNETISM       [PT.  i.  274 

and  chest  muscles  serving  to  start  respiration.  Since  the 
discovery  of  the  Ley  den  jar  many  attempts  have  been  made 
to  establish  an  electrical  medical  treatment.  Discontinuous 
currents,  particularly  those  furnished  by  small  induction- 
coils  and  magneto-electric  machines,  are  employed  by  prac- 
titioners to  stimulate  the  nerves  in  paralysis  and  other 
affections.  Living  muscle  when  stimulated  by  a  single 
shock  such  as  a  single  spark  from  an  electric  machine  causes 
a  single  muscular  twitch,  the  contraction  lasting  about  y1^ 
second.  A  rapid  succession  of  shocks,  such  as  is  given  by 
an  induction  coil  or  an  alternating  current,  causes  a  succes- 
sion of  contractions  which  blend  into  a  permanent  state  of 
contraction  which  lasts  as  long  as  the  stimulating  cause  is 
applied.  When  a  continuous  current  is  used,  not  exceeding 
4  or  5  milliamperes,  there  is  a  twitch  on  making  the  circuit 
followed  by  a  relaxation  that  lasts  as  long  as  the  current 
lasts,  but  with  another  twitch  when  the  circuit  is  broken. 
With  currents  of  16  to  25  milliamperes  the  contraction  is 
permanent  till  the  current  is  cut  off.  In  certain  kinds  of 
paralysis  all  irritability  of  muscle  disappears.  Application 
of  electric  stimulus  in  health  generally  slightly  increases 
muscular  power,  and  in  debility  after  illness  may  aid  nutrition. 
The  usual  pathological  dose  of  current  is  from  2  to  10 
milliamperes.  Apparatus  pretending  to  cure,  and  incapable 
of  furnishing  such  currents,  is  worthless.  Continuous  cur- 
rents appear  to  produce  a  sedative  effect  around  the  anode, 
which  is  of  service  in  neuralgia  and  painful  affections,  and 
an  increase  in  irritability  around  the  kathode,  useful  in  cer- 
tain cases  of  paralysis.  In  cases  of  paralysis  due  to  lesion 
of  nerve  connexions  or  degeneration  of  nerve  centres  elec- 
tricity is  unavailing.  The  continuous  current  is  also  em- 
ployed electrolytically  to  disperse  tumours.  Alternating 
currents,  and  rapidly  interrupted  uni-directional  currents, 
stimulate  the  nerves.  Bare  metal  electrodes  must  never  be 
allowed  to  touch  the  skin  unless  the  object  is  to  produce 
sores.  They  should  be  covered  with  moist  washleather. 


CH.  in.  275]  MEDICAL  APPLICATIONS  239 

275.  Physiological  Action  of  Magnets.  —  Magnets  exer- 
cise no  physiological  action  whatever,  and  the  wearing  of 
magnets  in  belts,  armlets,  or  rings  is  of  no  curative  value 
whatever.  The  author  of  these  Lessons  has  however  shown  l 
that  a  rapidly-alternating  magnetic  field  applied  to  the  head 
produces  certain  curious  phenomena  as  of  flickering  lights  in 
the  perception  of  vision.  This  is  probably  due  to  the  induc- 
tion of  eddy-currents  (Art.  500)  in  the  optic  nerves,  and 
hence  is  electrical,  not  magnetic. 

1  See  Proceedings  of  the  Royal  Society,  vol.  Ixxxii,  p.  396,  1910. 


Part  Second 
CHAPTER  IV 

ELECTROSTATICS 

LESSON  XXI.  —  Theory  of  Potential 

276.  By  the  lessons  in  Chapter  I.  the  student  will  have 
obtained  some  elementary  notions  upon  the  existence  and 
measurement  of  definite  quantities  of  electricity.     In  the 
present  lesson,  which  is  both  one  of  the  hardest  and  one  of 
the  most  .important  to  the  beginner,  and  which  he  must 
therefore  study  the  more  carefully,  the  laws  which  concern 
the  magnitude  of  electrical  quantities  and  their  measure- 
ment are  more  fully  explained.     In  no  branch  of  knowledge 
is  it  more  true  than  in  electricity,  that  "  science  is  measure- 
ment."    That  part  of  the  science  of  electricity  which  deals 
with  the  measurement  of  charges  of  electricity  is  called 
Electrostatics.     We  shall  begin  by  discussing  first  the  fun- 
damental laws  of  electric  force,  which  were  brought  to  light 
in  Chapter  I.  by  simple  experimental  means. 

277.  First    Law    of    Electrostatics.  —  Electric    charges    of 
similar  sign  repel  one  another,  but  electric  charges  of  opposite 
signs  attract  one  another.     The  fundamental  facts  expressed 
in  this  Law  were    fully  explained    in    Lesson  I.     Though 
familiar  to  the  student,  and  apparently  simple,  these  facts 
require  for  their  complete  explanation  the  aid  of  advanced 
mathematical  analysis.     They  will  here  be  treated  as  simple 
facts  of  observation. 

278.  Second   Law  of  Electrostatics.  —  The  force  exerted 
between  two  charges  of  electricity  (supposing  them  to  be  col- 

240 


CH.  iv.  279]  ELECTRIC   QUANTITY  241 

lected  at  points  or  on  two  small  spheres)  is  directly  propor- 
tional to  their  product  and  inversely  proportional  to  the  square 
of  the  distance  between  them.  This  law,  discovered  by  Cou- 
lomb, and  called  Coulomb's  Law,  was  briefly  alluded  to 
(on  p.  Ill)  in  the  account  of  experiments  made  with  the 
torsion-balance;  and  examples  were  then  given  in  illustra- 
tion of  both  parts  of  the  law.  We  saw,  too,  that  a  similar 
law  held  good  for  the  forces  exerted  between  two  magnetic 
point-poles.  Coulomb  applied  the  method  of  oscillations  to 
verify  the  indications  of  the  torsion-balance  and  found  the 
results  entirely  confirmed.  We  may  express  the  two  clauses 
of  Coulomb's  Law  in  the  following  symbolic  manner.  Let  / 
stand  for  the  force,  q  for  the  quantity  of  electricity  in  one 
of  the  two  charges,  and  qf  for  that  of  the  other  charge,  and 
let  r  stand  for  the  distance  between  them.  Then, 

(1)  /  is  proportional  to  q  X  qr, 
and  (2)  /  is  proportional  to  —  . 

Choosing  our  units  so  that  these  two  expressions  may  be 
combined  into  one,  we  may  write  our  symbols  as  an  equa- 
tion :  — 


279.  Unit  of  Electric  Quantity.  —  This  equality  is  correct 
if  our  unit  of  electricity  is  chosen  to  accord  with  the  units 
already  fixed  for  measuring  force  and  distance.  Electricians 
of  all  nations  have  agreed  in  adopting  a  system  based  upon 
three  fundamental  units  :  viz.  the  Centimetre  as  the  unit  of 
length;  the  Gramme  as  the  unit  of  mass;  the  Second  as  the 
unit  of  time.  All  other  units  can  be  derived  from  these,  as 
is  explained  in  the  Note  at  the  end  of  this  Lesson,  pp.  258 
to  260.  Now,  amongst  the  derived  units  of  this  system  is 
the  unit  of  force,  named  the  Dyne,  which  is  that  force  which, 
acting  for  one  second  on  a  mass  of  one  gramme,  imparts  to 
it  a  velocity  of  one  centimetre  per  second.  Taking  the  dyne 
R 


242  ELECTRICITY   AND   MAGNETISM      [PT.  n.  280 

as  the  unit  of  force,  and  the  centimetre  as  the  unit  of  length 
(or  distance),  we  must  find  for  our  equation  a  unit  of  electric 
quantity  to  agree  with  them.  If  q,  q' ,  and  r  have  each  of 
them  unit  value  (that  is,  if  we  took  two  charges  of  value  1 
each,  and  placed  them  one  centimetre  apart),  the  value  of 

^-p  would  be  ,  which  is  equal  to  1.     Hence  our  Defi- 

T"  L    /\   1 

nition  of  a  Unit  of  Electricity  l  is  :  —  One  Unit  of  Electricity 
is  that  quantity  which,  when  placed  at  a  distance  of  one  centi- 
metre (in  air)  from  a  similar  and  equal  quantity,  repels  it  with 
a  force  of  one  dyne. 

An  example  will  aid  the  student  to  understand  the  appli- 
cation of  Coulomb's  Law. 

Example.  —  Two  small  spheres,  charged  respectively  with 
6  units  and  8  units  of  -f  electricity,  are  placed  4  centi- 
metres apart ;  find  what  force  they  exert  on  one  another.  By 

the  formula,  /  =  flL^,  we  find  /  =  ^8=||=3  dynes. 

The  force  in  the  above  example  would  clearly  be  a  force 
of  repulsion.  Had  one  of  these  charges  been  negative,  the 
product  q  X  q'  would  have  had  a  —  value,  and  the  answer 
would  have  come  out  as  minus  3  dynes.  The  presence  of  the 
negative  sign,  prefixed  to  a  force,  will  indicate  that  it  is  a 
force  of  attraction,  whilst  the  plus  sign  would  signify  a  force 
of  repulsion. 

The  intensity  of  an  electric  field  (Art.  283)  being  measured 
by  the  force  it  exerts  on  a  unit  charge,  it  at  once  follows 
that  at  a  distance  of  r  (in  air)  from  a  charge  q  the  intensity 
of  the  electric  field  due  to  that  charge  will  be  q/r2.  If  the 
intervening  medium  be  not  air,  but  have  a  specific  dielectric 
capacity  k  (see  p.  277),  the  field  will  be  only  q/kr2. 

280.  Potential.  —  We  must  next  define  the  term  poten- 
tial, as  applied  to  electric  forces ;  but  to  make  the  meaning 

1  That  is,  one  unit  in  the  electrostatic  system.  It  is  only  ,)0oo, 000,000 
of  the  quantity  called  1  coulomb.  (See  Art.  301,  p.  260.) 


CH.  iv.  280]  ELECTRIC   POTENTIAL  243 

plain  a  little  preliminary  explanation  is  necessary.  Suppose 
we  had  a  -+-  charge  on  a  small  insulated  sphere  A  (see  Fig. 
158),  placed  by  itself  far  from  all  other  electric  charges  and 
conductors.  If  we  were  to  bring  another  positively-charged 
body  B  near  it,  A  would  repel  B.  But  the  repelling  force' 
would  depend  on  the  quantity  of  the  new  charge,  and  on  the 
distance  at  which  it  was  placed.  Suppose  the  new  charge 
thus  brought  near  to  be  one  +  unit ;  when  B  was  a  long 
way  off  it  would  be  repelled  with  a  very  slight  force,  and 
very  little  work  need  be  expended  in  bringing  it  up  nearer 
against  the  repelling  forces  exerted  by  A;  but  as  B  was 
brought  nearer  and  Clearer  to  A,  the  repelling  force  would 

6P             Q              B"  B' 
o Q- -0 -e — 

FIG.  158. 

grow  greater  and  greater,  and  more  and  more  work  would 
have  to  be  done  against  these  opposing  forces  in  bringing  up 
B.  Suppose  that  we  had  begun  at  an  infinite  distance  away, 
and  that  we  pushed  up  our  little  test  charge  B  from  B'  to 
B"  and  then  to  Q,  and  so  finally  moved  it  up  to  the  point  P, 
against  the  opposing  forces  exerted  by  A,  we  should  have 
had  to  spend  a  certain  amount  of  work;  that  work  represents 
the  potential 1  at  the  point  P  due  to  A.  For  the  following  is 
the  definition  of  electric  potential :  —  The  potential  at  any 
point  is  the  work  that  must  be  spent  upon  a  unit  of  positive 
electricity  in  bringing  it  up  to  that  point  from  an  infinite  dis- 
tance. Had  the  charge  on  A  been  a  —  charge,  the  force 
would  have  been  one  of  attraction,  in  which  case  we  should 
have  theoretically  to  measure  the  potential  at  P,  either  by 

1  In  its  widest  meaning  the  term  "potential"  must  be  understood  as 
"power  to  do  work."  For  if  we  have  to  do  a  certain  quantity  of  work 
against  the  repelling  force  of  a  charge  in  bringing  up  a  unit  of  electricity 
from  an  infinite  distance,  just  so  much  work  has  the  charge  power  to  do, 
for  it  will  spend  an  exactly  equal  amount  of  work  in  pushing  the  unit  of 
electricity  back  to  an  infinite  distance.  If  we  lift  a  pound  five  feet  high 
against  the  force  of  gravity,  the  weight  of  the  pound  can  in  turn  do  five 
foot-pounds  of  work  in  falling  back  to  the  ground. 


244  ELECTRICITY  AND   MAGNETISM     [PT.  n.  281 

the  opposite  process  of  placing  there  a  +  unit,  and  then 
removing  it  to  an  infinite  distance  against  the  attractive 
forces,  or  else  by  measuring  the  amount  of  work  which 
would  be  done  by  a  +  unit  in  being  attracted  up  to  P  from 
an  infinite  distance. 

It  can  be  shown  that  where  there  are  more  electrified 
bodies  than  one  to  be  considered,  the  potential  due  to  them 
at  any  point  is  the  sum  of  the  potentials  (at  that  point)  of 
each  one  taken  separately. 

It  can  also  be  shown  1  that  the  potential  at  a  point  P, 
near  an  electrified  particle  A,  is  equal  to  the  quantity  of 
electricity  at  A  divided  by  the  distance  between  A  and  P. 
Or,  if  the  quantity  be  called  q,  and  the  distance  r,  the  poten- 
tial is  q  -T-  r. 

281.  Proof.  —  First  determine  the  difference  of  potential  be- 
tween point  P  and  point  Q  due  to  a  charge  of  electricity  q  on  a 
small  sphere  at  A. 

Call  distance  AP  =  r,  and  AQ  =  r'.  Then  PQ  =  r'  -  r.  The 
difference  of  potential  between  Q  and  P  is  the  work  done  in  moving 
a  +  unit  from  Q  to  P  against  the  force ;  and  since 

work  =  (average)    force  X  distance    through    which  it 

is  overcome 
Vp  -  VQ  =  f(rf  -  r). 
Force  at  P  exerted  by  q  on  a  +  unit  =  <?/r2, 

and  the  force  at   Q  exerted  by  q  on  a  +  unit  =  g/r'2. 

A  f 

? 


FIG.  159. 

Suppose  now  that  the  distance  PQ  be  divided  into  any  number 

(n)  of  equal  parts  m,  rir2>  r2r3, Tn-\r'. 

The  force  at  r  =  q/rz. 

The  force  at  n  =  q/n2  ....  etc. 

1  The  complete  proof  would  require  an  elementary  application  of  the 
integral  calcujus,  but  an  easy  geometrical  demonstration,  sufficient  for 
present  purposes,  is  given  below. 


CH.  iv.  281]        DIFFERENCE    OF   POTENTIALS  245 

Now  since  ri  may  be  made  as  close  to  r  as  we  choose,  if  we  only 
take  n  a  large  enough  number,  we  shall  commit  no  serious  error 
in  supposing  that  r  X  n  is  a  fair  mean  between  r2  and  r^ :  hence 
we  may  assume  the  average  force  over  the  short  length  from 

r  to  n  to  be-^-. 

TTi 

Hence  the  work  done  in  passing  from  r\  to  r  will  be 


On  a  similar  assumption,  the  work  done  in  passing  from  r2  to 
TI  will  be 

=  of  ---  ]  ,  and  that  done  from  r3  to  r2  will  be 
\n     rj 

—  qf  ---  V  etc.,  giving  us  n  equations,  of  which  the 
\r2     rj 

last  will  be  the  work  done  in  passing  from  r'  to  rn_i 


Adding  up  all  these  portions  of  the  work,  the  intermediate 
values  of  r  cancel  out,  and  we  get  for  the  work  down  in  passing 
from  Q  to  P 


Next  suppose  Q  to   be  an  infinite  distance  from  A.     Here  r' 
infinity,  and  —  =  0.     In  that  case  the  equation  becomes 


If  there  are  a  number  of  electrified  particles  at  different 
distances  from  P,  the  potential  due  to  each  individual  charge 
is  unaffected  by  the  presence  of  the  other  charges,  and  there- 
fore the  potential  at  P  can  be  found  by  dividing  the  quantity  of 
each  charge  by  its  distance  from  the  point  P,  and  then  adding 
up  together  the  separate  amounts  so  obtained.  The  symbol  V 


246          ELECTRICITY   AND   MAGNETISM    [PT.  n.  282-284 

is  generally  used  to  represent  potential.     The  potential  at 
P  we  will  call  VP,  then 


..-.. 

or  VP  =  S^ 

This  expression  2q/r  represents  the  work  done  on  or  by 
(according  as  the  potential  at  P  is  positive  or  negative),  a 
unit  of  +  electricity  when  moved  up  to  the  given  point  P 
from  an  infinite  distance. 

282.  Zero  Potential.  —  At  a  place  infinitely  distant  from 
all  electrified  bodies  there  would  be  no  electric  forces  and 
the  potential  would  be  zero.     For  purposes  of  convenience 
it  is,  however,  usual  to  consider  the  potential  of  the  earth 
as  an  arbitrary  zero,  just  as  it  is  convenient  to  consider  "  sea- 
level  "  as  a  zero  from  which  to  measure  heights  or  depths 
(see  Art.  287). 

283.  Difference    of    Potentials.  —  Since   potential   repre- 
sents the  work  that  must  be  done  on  a  +  unit  in  bringing 
it  up  from  an  infinite  distance,  the  difference  of  potential 
between  two  points  is  the  work  to  be  done  on  or  by  a  +  unit 
of  electricity  in  carrying  it  from  one  point  to  the  other.     Thus 
if  VP  represents  the  potential  at  P,  and  VQ  the  potential  at 
another  point  Q,  the  difference  of  potentials  VP  —  VQ  de- 
notes the  work  done  in  moving  up  the  -f-  unit  from  Q  to  P. 
It  is  to  be  noted  that  since  this  value  depends  only  on  the 
values  of  the  potential  at  P  and  at  Q,  and  not  on  the  values 
at  intermediate  points,  the  work  done  will  be  the  same, 
whatever  the  path  along  which  the  particle  moves  from  Q 
to  P.     In  the  same  way  it  is  true  that  the  expenditure  of 
energy  in  lifting  a  pound  (against  the  earth's  attraction) 
from  one  point  to  another  on  a  higher  level,  will  be  the  same 
whatever  the  path  along  which  the  pound  is  lifted. 

284.  Electric  Force.  —  The  definition  of  "  work  "  is  the 
product  of  the  force  overcome  into  the  distance  through 


CH.  iv.  285]          EQUIPOTENTIAL   SURFACES  247 

which  the  force  is  overcome  ;    or  work  =  force  X  distance 
through  which  it  is  overcome. 

Hence,  if  the  difference  of  potential  between  two  points 
is  the  work  done  in  moving  up  our  +  unit  from  one  point 
to  the  other,  it  follows  that  the  average  electric  force  between 
those  points  will  be  found  by  dividing  the  work  so  done  by 

the   distance   between   the   points  ;    or      P          Q  =  /    (the 


average  electric  force  along  the  line  PQ).  The  (average) 
electric  force  is  therefore  the  rate  of  change  of  potential  per 
unit  of  length.  If  P  and  Q  are  near  together  the  force  will 
be  practically  uniform  between  P  and  Q.  The  term  poten- 
tial gradient,  or  electromotive  intensity,  is  sometimes  used  for 
the  force  in  an  electric  field. 

We  may  map  out  the  intensity  of  the  electric  field  at  any 
point  by  supposing  the  number  of  electric  lines  of  force 
passing  perpendicularly  through  one  square  centimetre  to 
represent  the  number  of  dynes  of  force  on  a  +  unit  placed 
at  the  point. 

285.  Equipotential  Surfaces.  —  A  charge  of  electricity 
collected  on  a  small  sphere  acts  on  external  bodies  as  if  the 
charge  were  all  collected  into  one  point  at  its  centre.1  We 
have  seen  that  the  force  exerted  by  such  a  charge  falls  off 
at  a  distance  from  the  ball,  the  force  becoming  less  and  less 
as  the  square  of  the  distance  increases.  But  the  force  is  the 
same  in  amount  at  all  points  equally  distant  from  the  small 
charged  sphere.  And  the  potential  is  the  same  at  all  points 
that  are  equally  distant  from  the  charged  sphere.  If,  in 
Fig.  159,  the  point  A  represents  the  sphere  charged  with  q 
units  of  electricity,  then  the  potential  at  P,  which  we  will 
call  VP,  will  be  equal  to  q/r,  where  r  is  the  distance  from  A 

1  The  student  must  be  warned  that  this  ceases  to  be  true  if  other  charges 
are  brought  very  near  to  the  sphere,  for  then  the  electricity  will  no  longer 
be  distributed  uniformly  over  its  surface.  It  is  for  this  reason  that  we  have 
said,  in  describing  the  measurement  of  electrical  forces  with  the  torsion 
balance,  that  "the  balls  must  be  very  small  in  proportion  to  the  distances 
between  them." 


248  ELECTRICITY   AND   MAGNETISM        [PT.  n.  285 

to  P.     But  if  we  take  any  other  point  at  the  same  distance 
from  A  its  potential  will  also  be  q/r.     Now  all  the  points 
that  are  the  same  distance  from  A  as  P  is,  will  be  found  to 
lie  upon  the  surface  of  a  sphere  whose  centre  is  at  A,  and 
which  is  represented  by  the  circle  drawn  through  P,  in  Fig. 
160.     All  round  this  circle  the  potential  will  have  equal 
values ;  hence  this  circle  represents  an  equipotential  surface. 
The  work  to  be  done  in  bringing  up  a  +  unit  from  an  infinite 
distance  will  be  the  same,  no  matter  what  point  of  this  equi- 
potential surface  it  is  brought  to,  and  to  move  it  about  from 
one  point  to  another  in  the  equipotential  surface  requires  no 
further  overcoming  of  the  electrical  forces,   and  involves 
therefore  no  further 

expenditure  of  work.          ,-''"          ~^\        \  \  \ 

At  another  distance, 

say  at  the  point  Q,    /       /  \       N\       \ 

the     potential     will   [       f         •        F     J9     j 
have  another  value,    \       \  j      j       j          j  \ 

and     through     this     \     ^......-"'/     /       /          /  / 

point  Q  another  equi-        \  ^/       /'          /  / 

potential  surface  may 

be  drawn.     Suppose  FlG- 16°- 

we  chose  Q  so  far  from  P  that  to  push  up  a  unit  of  +  elec- 
tricity against  the  repelling  force  of  A  required  the  expendi- 
ture of  just  one  erg  of  work  (for  the  definition  of  one  erg 
see  the  Note  on  Units  at  the  end  of  this  lesson) ;  there  will 
be  then  unit  difference  of  potential  between  the  surface 
drawn  through  Q  and  that  drawn  through  P,  and  it  will 
require  one  erg  of  work  to  carry  a  +  unit  from  any  point  on 
the  one  surface  to  any  point  on  the  other.  In  like  manner 
we  might  construct  a  whole  system  of  equipotential  surfaces 
about  the  point  A,  choosing  them  at  such  distances  that 
there  should  be  unit  difference  of  potential  between  each 
one  and  the  next.  The  widths  between  them  would  get 
wider  and  wider,  for,  since  the  force  falls  off  as  you  go 
farther  from  A,  you  must,  in  doing  one  erg  of  work,  bring 


CH.  iv.  286,  287]    POTENTIAL   INSIDE    CONDUCTORS     249 

up  the  +  unit  through  a  longer  distance  against  the  weaker 
opposing  force. 

The  form  of  the  equi potential  surfaces  about  two  small 
electrified  bodies  placed  near  to  one  another  would  not  be 
spherical ;  and  around  a  number  of  electrified  bodies  placed 
near  to  one  another  the  equipotential  surfaces  would  be  highly 
complex  in  form. 

286.  Lines   of   Force.  —  The   electric   force,    whether   of 
attraction  or  repulsion,  always  acts  across  the  equipotential 
surfaces  in  a  direction  normal  to  the  surface.     The  lines 
which  mark  the  direction  of  the  resultant  electric  forces  are 
sometimes  called  lines  of  electric  force.     In  the  case  of  the 
single  electrified  sphere  the  lines  of  force  would  be  straight 
lines,    radii    of   the    system    of    equipotential    spheres.     In 
general,  however,  lines  of  force  are  curved ;   in  this  case  the 
resultant  force  at  any  point  would  be  in  the  direction  of  the 
tangent  to  the   curve  at  that  point.      Two  lines  of  force 
cannot  cut  one  another,  for  the  resultant  force  at  a  point 
cannot  act  in  two  directions  at  once.     The  positive  direction 
along  a  line  of  force  is  that  direction  in  which  a  small  posi- 
tively-charged body  would  be  impelled  by  the  electric  force 
if  free  to  move.     A  space  bounded  by  a  number  of  lines  of 
force  is  sometimes  spoken  of  as  a  tube  of  force.     All  the  space, 
for  example,  round  a  small  insulated  electrified  sphere  may 
be  regarded  as  mapped  out  into  a  number  of  conical  tubes, 
each  having  its  apex  at  the  centre  of  the  sphere.     The  total 
electric  force  exerted  across  any  section  of  a  tube  of  force  is 
constant  wherever  the  section  be  taken. 

287.  Potential  within  a  Closed  Conductor.  —  The  experi- 
ments related  in  Arts.  32  to  36  prove  most  convincingly 
that  there  is  no  electric  force  inside  a  closed  conductor  due  to 
charges  outside  or  on  the  surface  of  the  conductor.     Now  we 
have  shown  above  that  electric  force  is  the  rate  of  change  of 
potential  per  unit  of  length.     If  there  is  no  electric  force 
there  is  no   change  of  potential.     The  potential  within  a 
closed  conductor  (for  example,  a  hollow  sphere)  due  to  charges 


250  ELECTRICITY   AND   MAGNETISM       [PT.  H.  287 

outside  or  on  the  surface  is  therefore  the  same  all  over  the 
interior ;  the  same  as  the  potential  of  the  surface.  The  sur- 
face of  a  closed  conductor  is  necessarily  an  equipotential  sur- 
face. If  it  were  not  at  one  potential  there  would  be  a  flow 
of  electricity  from  the  higher  potential  to  the  lower,  which 
would  instantaneously  establish  equilibrium  and  reduce  the 
whole  to  one  potential.  The  student  should  clearly  distin- 
guish between  the  surface-density  at  a  point,  and  the  poten- 
tial at  that  point  due  to  neighbouring  charges  of  electricity. 
We  know  that  when  an  electrified  body  is  placed  near  an 
insulated  conductor  the  nearer  and  farther  portions  of  that 
conductor  exhibit  induced  charges  of  opposite  kinds.  Yet 
all  is  at  one  potential.  If  the  +  and  —  charges  on  the  con- 
ductor had  not  separated  by  a  movement  of  electricity  from 
one  side  to  the  other,  a  difference  of  potential  would  exist 
between  those  sides  because  they  are  at  different  distances 
from  the  electrified  body.  But  that  is  a  state  of  affairs 
which  could  not  continue  in  the  conductor,  for  the  difference 
of  potential  would  cause  electricity  to  flow  until  the  com- 
bined potential  due  to  the  electrified  body  and  the  charges  at 
the  opposite  sides  was  the  same  at  every  point  in  the  conductor. 

The  potential  at  any  point  in  a  conducting  sphere  (hollow 
or  solid)  due  to  an  electrified  particle  A,  situated  at  a  point 
outside  (Fig.  162),  is  equal  to  the  quantity  of  electricity  q  at 
A  divided  by  the  distance  between  A  and  the  centre  of  the 
sphere.  For  if  B  be  the  centre  of  the  sphere,  the  potential 
at  B  due  to  q  is  q/r,  where  r  =  AB ;  but  all  points  in  the 
sphere  are  at  the  same  potential,  therefore  they  are  all  at 
the  potential  q/r. 

The  earth  is  a  large  conducting  sphere.  Its  potential, 
due  to  a  positive  charge  q  near  to  its  surface,  is  q/r,  where 
r  may  be  taken  as  the  radius  of  the  earth ;  that  is,  636,000,000 
centimetres.  But  it  is  impossible  to  produce  a  +  charge 
q  without  generating  also  an  equal  negative  charge  —  q;  so 
the  potential  of  the  earth  due  to  both  charges  is  q/r  —  q/r 
=  0  (see  Art.  282). 


CH.  iv.  288, 289]  CAPACITY  251 

288.  Law    of   Inverse    Squares. — An   important  conse- 
quence follows  from  the  absence  of  electric  force  inside  a 
closed  conductor  due  to  a  charge  on  its  surface;    this  fact 
enables   us   to   demonstrate    the    necessary    truth    of   the 
"  law  of  inverse  squares  "  which  was 

first  experimentally,  though  roughly, 
proved  by  Coulomb  with  the  torsion 
balance.  Suppose  P  to  be  a  point 
anywhere  inside  a  hollow  sphere 
charged  with  electricity  (Fig.  161). 
The  charge  is  uniformly  distributed 
over  the  surface  of  the  sphere  and  the 
quantity  of  electricity  on  any  small 
portion  will  be  proportional  to  the 

area  of  that  portion.  Consider  a  small  portion  of  the  sur- 
face AB.  The  charge  on  AB  would  repel  a  +  unit  placed 
at  P  with  a  certain  force.  Now  draw  the  lines  AD  and  BC 
through  P,  and  regard  these  as  mapping  out  a  small  conical 
surface  of  two  sheets,  having  its  apex  at  P;  the  small  area 
CD  will  represent  the  end  of  the  opposed  cone,  and  the 
electricity  on  CD  will  also  act  on  the  +  unit  placed  at  P, 
and  repel  it.  Now  these  areas  AB  and  CD,  and  the  charges 
on  them,  will  be  directly  proportional  to  the  squares  of  their 
respective  distances  from  P.  If,  then,  the  forces  which  they 
exercise  on  P  exactly  neutralize  one  another  (as  experiment 
shows  they  do),  it  is  clear  that  the  electric  force  must  fall 
off  inversely  as  the  squares  of  the  distances;  for  the  whole  sur- 
face of  the  sphere  can  be  mapped  out  similarly  by  imaginary 
cones  drawn  through  P.  The  reasoning  can  be  extended  also 
to  hollow  conductors  of  any  form. 

289.  Capacity.  —  In   Lesson   IV.   the  student  was   given 
some  elementary  notions  on  the  subject  of  the  Capacity  of 
conductors.     We  are  now  ready  to  give  the  precise  defini- 
tion.    The  Electrostatic  Capacity  of  a  conductor  is  measured 
by  the  quantity  of  electricity  which  must  be  imparted  to  it  in 
order  to  raise  its  potential  from  zero  to  unity.     A  small  conduc- 


252  ELECTRICITY   AND   MAGNETISM      [PT.  n.  290 

tor,  such  as  an  insulated  sphere  of  the  size  of  a  pea,  will  not 
want  so  much  as  one  unit  of  electricity  to  raise  its  potential 
from  0  to  1 ;  it  is  therefore  of  small  capacity  —  while  a  large 
sphere  will  require  a  large  quantity  to  raise  its  potential  to 
the  same  degree,  and  would  therefore  be  said  to  be  of  large 
capacity.  If  C  stand  for  capacity,  and  Q  for  a  quantity  of 
electricity, 

C  =  Q  and  CV  =  Q. 

This  is  equivalent  to  saying  in  words  that  the  quantity 
of  electricity  necessary  to  charge  a  given  conductor  to  a 
given  potential  is  numerically  equal  to  the  product  of  the 
capacity  into  the  potential  through  which  it  is  raised.  The 
capacity  of  an  insulated  body  is  affected  by  the  presence 
of  neighbouring  conductors.  Whenever  we  speak  of  the 
capacity  of  a  body,  we  mean  of  that  body  when  isolated  as 
well  as  insulated. 

290.  Unit  of  Capacity.  —  A  conductor  that  required  only 
one  unit  of  electricity  to  raise  the  potential  between  it  and  the 
earth  from  0  to  1 ,  would  be  said  to  possess  unit  capacity.  A 
sphere  one  centimetre  in  radius  possesses  unit  capacity ;  for 
if  it  be  charged  with  a  quantity  of  one  unit,  this  charge  will 
act  as  if  it  were  collected  at  its  centre.  At  the  surface, 
which  is  one  centimetre  away  from  the  centre,  the  potential, 
which  is  measured  as  q/r,  will  be  1.  Hence,  as  1  unit  of 
quantity  raises  it  to  unit  1  of  potential,  the 
sphere  possesses  unit  capacity.  The  capaci- 
ties of  spheres  (isolated  in  air)  are  proportional 
to  their  radii.  We  may  imagine  the  charge  q 
(Fig.  162)  being  brought  nearer  and  nearer 
the  sphere  until  it  reaches  the  surface,  then 
r  becomes  the  radius  of  the  sphere.  We  may  further 
imagine  the  surface  completely  covered  with  little  quanti- 
ties q,  so  as  to  have  a  total  charge  Q  uniformly  distributed. 
Each  little  quantity  would  give  to  the  sphere  a  potential 
q/r;  the  total  potential  of  the  sphere  due  to  the  charge  Q 


CH.  iv.  291]    SURFACE-DENSITY   OF   CHARGES  253 

on  its  surface  would  be  Q/r.  The  greater  the  sphere  the 
less  would  be  the  potential  at  any  point  in  it  due  to  the 
same  charge  Q.  Thus  it  would  be  necessary  to  give  a 
charge  of  100  units  to  a  sphere  of  100  centimetres'  radius 
in  order  to  raise  its  potential  to  unity.  It  therefore  has  a 
capacity  of  100.  The  earth  has  a  capacity  of  about  630 
millions  (in  electrostatic  unit).1  It  is  difficult  to  calculate 
the  capacities  of  conductors  of  other  shapes.  It  must  be 
noted  that  the  capacity  of  a  sphere,  as  given  above,  means 
its  capacity  when  far  removed  from  other  conductors  or 
charges  of  electricity.  The  capacity  of  a  conductor  is 
increased  by  bringing  near  it  a  charge  of  an  opposite  kind ; 
for  the  potential  at  the  surface  of  the  conductor  is  the  sum 
of  the  potential  due  to  its  own  charge,  and  of  the  potential 
of  opposite  sign  due  to  the  neighbouring  charge.  Hence,  to 
bring  up  the  resultant  potential  to  unity,  a  larger  quantity 
of  electricity  must  be  given  to  it ;  or,  in  other  words,  its 
capacity  is  greater.  This  is  the  true  way  of  regarding  the 
action  of  Leyden  jars  and  other  condensers,  and  must  be  re- 
membered by  the  student  when  he  advances  to  the  considera- 
tion of  the  theory  of  condenser  action,  in  Lesson  XXIII. 

291.  Surface-Density.2  —  Coulomb  applied  this  term  to 
denote  the  amount  of  electrification  per  unit  of  area  at  any 
point  of  a  surface.  It  was  mentioned  in  Lesson  IV.  that  a 
charge  of  electricity  was  never  distributed  uniformly  over  a 
conductor,  except  in  the  case  of  an  insulated  sphere.  Where 
the  distribution  is  unequal,  the  density  at  any  point  of  the 
surface  may  be  expressed  by  considering  the  quantity  of 

1  Or  about  700  microfarads  (see  Art.  301). 

2  The  word  Tension  is  sometimes  used  for  that  which  is  here  precisely 
defined  as  Coulomb  defined  it.     The  term  tension  is,  however,  unfortunate ; 
and  it  is  so  often  misapplied  in  text-books  to  mean  not  only  surface  density 
but  also  potential,  and  even  electric  force  (i.e.  the  mechanical  force  exerted 
upon  a  material  body  by  electricity),  that  we  might  well  avoid  its  use  alto- 
gether.    The  term  would  be  invaluable  if  we  might  adopt  it  to  denote  only 
the  mechanical  stress  across  a  dielectric,  as  in  Art.  297.     This  was  Maxwell's 
use  of  the  word,  denoting  a  pulling  force  distributed  over  an  area,  just  as 
the  word  pressure  means  a  distributed  pushing  force. 


254  ELECTRICITY  AND   MAGNETISM      [PT.  n.  292 

electricity  which  exists  upon  a  small  unit  of  area  at  that 
point.  If  Q  be  the  quantity  of  electricity  on  the  small  sur- 
face, and  S  be  the  area  of  that  small  surface,  then  the  surface- 
density  (denoted  by  the  Greek  letter  p)  will  be  given  by  the 
equation, 

P=S 

S 

In  dry  air,  the  limit  to  the  possible  electrification  is  reached 
when  the  density  reaches  the  value  of  about  20  units  of 
electricity  per  square  centimetre.  If  charged  to  a  higher 
degree  than  this,  the  electricity  escapes  in  "  brushes  "  into 
the  air.  In  the  case  of  uniform  distribution  over  a  surface 
(as  with  the  sphere,  and  as  approximately  obtained  on  a 
flat  disk  by  a  particular  device  known  as  a  guard-ring),  the 
density  is  found  by  dividing  the  whole  quantity  of  the  charge 
by  the  whole  surface. 

292.  Surface-Density  on  a  Sphere.  —  The  surface  of  a 
sphere  whose  radius  is  r,  is  4  irr2.  Hence,  if  a  charge  Q  be 
imparted  to  a  sphere  of  radius  r,  the  surface-density  will  be 
p  =  Q  -f-  4  7TT2 ;  or,  if  we  know  the  surface-density,  the 
quantity  of  the  charge  will  be  Q  =  4  irr2p. 

The  surface-density  on  two  spheres  joined  by  a  thin  wire 
is  an  important  case.  If  the  spheres  are  unequal,  they  will 
share  the  charge  in  proportion  to  their  capacities  (see  Art. 
40),  that  is,  in  proportion  to  their  radii.  If  the  spheres  are 
of  radii  2  and  1,  the  ratio  of  their  charges  will  also  be  as  2  to 
1.  But  their  respective  densities  will  be  found  by  dividing 
the  quantities  of  electricity  on  each  by  their  respective  sur- 
faces. But  the  surfaces  are  proportional  to  the  squares  of 
the  radii,  i.e.  as  4 :  1 ;  hence,  the  densities  will  be  1:2,  or 
inversely  as  the  radii.  Now,  if  one  of  these  spheres  be  very 
small  —  no  bigger  than  a  point  —  the.  density  on  it  will  be 
relatively  immensely  great,  so  great  that  the  air  particles  in 
contact  with  it  will  rapidly  carry  off  the  charge  by  convec- 
tion. This  explains  the  action  of  points  in  discharging  con- 
ductors, noticed  in  Chapter  I.,  Arts.  38,  45,  and  47. 


CH.  iv.  293, 294]   FORCE   NEAR  A   CHARGED   SPHERE  255 

293.  Electric  Images.  —  It  can  be   shown   mathematically  that 
if  +  q  units   of    electricity   are   placed   at   a   point    near   a   non- 
insulated  conducting  sphere  of  radius  r,  at  a  distance  d  from  its 
centre,  the  negative  induced  charge  will  be  equal    to  —  qr/d,  and 
will  be  distributed  over  the  nearest  part  of  the  surface  of  the  sphere 
with  a  surface-density  inversely  proportional   to  the  cube  of  the 
distance  from  that  point.     Lord  Kelvin  pointed  out  that,  so  far 
as  all  external  points  are  concerned,  the  potential  due  to  this  peculiar 
distribution  on  the  surface  would  be  exactly  the  same  as  if  this 
negative  charge  were  all  collected  at  an  internal  point  at  a   dis- 
tance of  r  —  r*/d  behind  the  surface.     Such  a  point  may  be  re- 
garded as  a  virtual  image  of  the  external  point,  in  the  same  way  as 
in  optics  we  regard  certain  points  behind  mirrors  as  the    virtual 
images  of  the  external  points  from  which  the  rays  proceed.     Clerk 
Maxwell  has  given  the  following  definition  of  an  Electric  Image :  — 
An  electric  image  is  an  electrified  point,  or  system  of  points,  on  one 
side  of  a  surface,  which  would  produce  on  the  other  side  of  that  surface 
the  same  electrical  action  which   the  actual  electrification  of  that  sur- 
face really  does  produce.      If   the  sphere  is  not  connected  to  earth, 
and  were  unelectrified  before  +  q  was  brought  near  it,  we  may  find 
the    surface-density   at   any   point   by   the   following   convention. 
Imagine  that  there  are  coexisting  on  the  sphere  two  charges,  —rq/d 
and  +  rq/d  respectively,  the  first  being  distributed  so  that  its  surface- 
density  is  inversely  proportional  to  the  cube  of  the  distance  from  the 
electrified  point,  and  the  second  being  uniformly  distributed.     The 
actual  surface-density  is  the  algebraic  sum  of  these  two.     A    + 
charge  of  electricity  placed  1  inch  in  front  of  a  flat  metallic  plate  in- 
duces on  it  a  negative  charge  distributed  over  the  neighbouring 
region  of  the  plate  (with  a  density  varying  inversely  as  the  cube  of 
the  distance  from  the  point) ;  but  the  electrical  action  of  this  distri- 
bution, so  far  as  all  points  in  front  of  the  plate  are  concerned,  would 
be  precisely  represented  by  its  "  image,"   namely,   by  an  equal 
quantity  of  negative  electricity  placed  at  a  point  1  inch  behind  the 
plate.     Many  beautiful  mathematical  applications  of  this  method 
have  been  made,  enabling  the  distribution  to  be  calculated  in  diffi- 
cult cases,  as,  for  example,  the  distribution  of  the  charge  on  the 
inner  surface  of  a  hollow  bowl. 

294.  Force  near  a  Charged  Sphere.  —  It  was  shown  above 
that  the  quantity  of   electricity  Q  upon  a  sphere  charged 
until  its  surface-density  was  p,  was 

Q  =  4  Trry 


256          ELECTRICITY  AND   MAGNETISM     [PT.  n.  295,  296 

The  problem  is  to  find  the  force  exercised  by  this  charge 
upon  a  +  unit  of  electricity,  placed  at  a  point  infinitely 
near  the  surface  of  the  sphere.  The  charge  on  the  sphere 
acts  as  if  at  its  centre.  The  distance  between  the  two 
quantities  is  therefore  r.  By  Coulomb's  Law  the  force 


This  important  result  may  be  stated  in  words  as  fol- 
lows :  —  The  force  (in  dynes)  exerted  by  a  charged  sphere 
upon  a  unit  of  electricity  placed  infinitely  near  to  its  surface, 
is  numerically  equal  to  4  TT  times  the  surface-density  of  the 
charge. 

295.  Force  near  a   Charged  Plate   of  indefinite   size.  - 
Suppose  a  plate  of  indefinite  extent  to  be  charged  so  that  it 
has  a  surface-density  p.     This  surface-density  will  be  uni- 
form, for  the  edges  of  the  plate  are  supposed  to  be  so  far  off 
as  to  exercise  no  influence.     It  can  be  shown  that  the  force 
exerted  by  such  a  plate  upon  a  +  unit  anywhere  near  it,  will 
be  expressed  (in  dynes)  numerically  as  2  TT/D.     This  will  be  of 
opposite  signs  on  opposite  sides  of  the  plate,  being  -j-  2  irp 
on  one  side,  and  —  2  irp  on  the  other  side,  since  in  the  two 
cases  the  force  tends  to  move  the  unit  in  opposite  directions. 
It  is  to  be  observed,  therefore,  that  the  force  changes  its 
value  by  the  amount  of  4  irp  as  the  point  passes  through 
the   surface.     The   same  was   true   of  the  charged  sphere, 
where   the   force   outside  was   4  TT/O,   and   inside    was   zero. 
The    same    is  true   of    all   charged   surfaces.      These  two 
propositions  are  of  the  utmost  importance  in  the  theory  of 
Electrostatics. 

296.  Proof   of    Theorem.  —  The   elementary  geometrical 
proof  is  as  follows  :  — 

Required  the  Electric  Force  at  a  point  at  any  distance  from  a 
plane  of  infinite  extent  charged  to  surface-density  p. 

Let  P  be  the  point,  and  PX  or  a  the  normal  to  the  plane.  Take 
any  small  cone  having  its  apex  at  P.  Let  the  solid  angle  of  this 


CH.  iv.  296]      FORCE   NEAR  A   CHARGED   PLATE  257 

cone  be  w ;  let  its  length  be  r ;  and  9  the  angle  its  axis  makes  with  a. 
The  cone  meets  the  surface  of  the  plane  obliquely  and  if  an  orthog- 


FIG.  163. 

onal  section  be  made  where  it  meets  the  plane  the  angle  between 
these  sections  will  be  =  9. 

orthogonal  area  of    section 
Now  solid  angle  w  is  by  definition  =  —  —  —  — 

Hence,  area  of  oblique  section  =  r2w  X  -  r 

cos  9 

/.  charge  on  oblique  section       =  --  -• 

Hence  if    a  +  unit  of    electricity  were  placed  at    P,   the    force 

exerted  on  it  by  this  small  charge      =    r  wpn  X  1  •*•  rz  =     up   • 

cos  9  cos  9 

Resolve  this  force  into  two  parts,  one  acting  along  the  plane,  the 
other  along  a,  normal  to  the  plane.     The  normal  component  along 


a  is  cos  9  X  --  -  =  tap. 
cos  B 

But  the  whole  surface  of  the  plane  may  be  similarly  mapped 
out  into  small  surfaces,  all  forming  small  cones,  with  their  summits 
at  P.  If  we  take  an  infinite  number  of  such  small  cones  meeting 
every  part,  and  resolve  their  forces  in  a  similar  way,  we  shall  find 
that  the  components  along  the  plane  will  neutralize  one  another 
all  round,  while  the  normal  components,  or  the  resolved  forces 
along  a,  will  be  equal  to  the  sum  of  all  their  solid  angles  multiplied 
by  the  surface  density  ;  or 

Total  resultant  force  along  a  =  Swp. 

But  the  total  solid  angle  subtended  by  an  indefinite  plane  at  a 
point  is  2  TT,  for  it  subtends  a  whole  hemisphere. 

.-.  Total  resultant  force  =  2  wp. 


258          ELECTRICITY  AND   MAGNETISM    [PT.  n.  297-299 

297.  Electric    Stress    in    Medium.  —  In    every    electric 
field  (Art.  13)  there  exists  a  tension  along  the  lines  of  electric 
force  accompanied  by  an  equal  pressure  in  all  directions  at 
right  angles  to  the  lines.     If  F  stands  for  the  resultant  electric 
force  on  a  +  unit  placed  at  any  point  in  the  field  (i.e.  the 
"  electromotive  intensity  "  at  that  point),  the  tension  will 
.be  equal  to  F2/8  w  (dynes  per  square  centimetre).     In  media 
having  dielectric  capacities  greater  than  unity  the  tension  is 
proportionally   greater.     For   the   optical    effects   of   these 
stresses  see  Art.  612. 

NOTE    ON    FUNDAMENTAL   AND    DERIVED    UNITS 

298.  Fundamental    Units.  —  All    physical    qualities,    such    as 
force,  velocity,  etc.,  can  be  expressed  in  terms  of  the  three  funda- 
mental quantities  :  length,  mass,  and  time.     Each  of  these  quantities 
must  be  measured  in  terms  of  its  own  units. 

The  system  of  units,  adopted  by  almost  universal  consent, 
and  used  throughout  these  lessons,  is  the  so-called  "  Centimetre- 
Gramme-Second  "  system,  in  which  the  fundamental  units  are :  — 

The  Centimetre  as  a  unit  of  length; 
The  Gramme  as  a  unit  of  mass; 
The  Second  as  a  unit  of  time. 

The  Centimeter  is  equal  to  0*3037  inch  in  length,  and  nominally 
represents  one  thousand-millionth  part,  or  i.ooo.o^o.ooo  of  a  quadrant 
of  the  earth. 

The  Metre  is  100  centimetres,  or  39*37  inches. 

The  Kilometre  is  1000  metres,  or  about  1093*6  yards. 

The  Millimetre  is  TV  of  a  centimetre,  or  0*03937  inch. 

The  Gramme  represents  the  mass  of  a  cubic  centimetre  of  water 
at  4°  C.,  this  is  equal  to  15*432  grains :  the  Kilogramme  is  1000 
grammes  and  corresponds  to  about  2*2  pounds. 

299.  Derived  Units.  - 

Area.  —  The  unit  of  area  is  the  square  centimetre. 

Volume.  —  The  unit  of  volume  is  the  cubic  centimetre. 

Velocity.  —  The  unit  of  velocity  is  the  velocity  of  a  body  which 

moves  through  unit  distance  in  unit  time,  or  the  velocity  of 

one  centimetre  per  second. 
Acceleration.  —  The   unit   of   acceleration   is   that   acceleration 

which  imparts  unit  velocity  to  a  body  in  unit  time,  or  an 


CH.  iv.  299]  DERIVED   UNITS  259 

acceleration  of  one  centimetre-per-second  per  second.  The 
acceleration  due  to  gravity  imparts  in  one  second  a  velocity 
considerably  greater  than  this,  for  the  velocity  it  imparts  to 
falling  bodies  is  about  981  centimetres  per  second  (or  about 
32 '2  feet  per  second).  The  value  differs  slightly  in  different 
latitudes.  At  Greenwich  the  value  of  the  acceleration  of 
gravity  is  g  =  981*1 ;  at  the  Equator  g  =  978' 1 ;  at  the 
North  Pole  g  =  983'1. 

Force.  —  The  unit  of  force  is  that  force  which,  acting  for  one 
second  on  a  mass  of  one  gramme,  gives  to  it  a  velocity  of 
one  centimetre  per  second.  It  is  called  one  Dyne.  The 
force  with  which  the  earth  attracts  any  mass  is  usually 
called  the  "  weight  "  of  that  mass,  and  its  value  obviously 
differs  at  different  points  of  the  earth's  surface.  The 
force  with  which  a  body  gravitates,  i.e.  its  weight  (in  dynes), 
is  found  by  multiplying  its  mass  (in  grammes)  by  the  value 
of  g  at  the  particular  place  where  the  force  is  exerted. 
One  pound  force  in  England  is  about  445,000  dynes. 

Work.  —  The  unit  of  work  is  the  work  done  in  overcoming 
unit  force  through  unit  distance,  i.e.  in  pushing  a  body 
through  a  distance  of  one  centimetre  against  a  force  of  one 
dyne.  It  is  called  one  Erg.  Since  the  "  weight  "  of  one 
gramme  is  1  X  981  or  981  dynes,  the  work  of  raising  one 
gramme  through  the  height  of  one  centimetre  against  the 
force  of  gravity  is  981  ergs.  One  foot-pound  of  work  (at 
London),  that  is  the  work  done  in  raising  one  pound  one 
foot  high  against  the  force  of  gravity  (at  London),  equals 
13,563,000  ergs. 

Energy.  —  The  unit  of  energy  is  also  the  erg;  for  the  energy  of 
a  source  is  measured  by  the  work  it  can  do. 

Power.  —  Power  being  the  rate  at  which  work  is  being  done,  the 
unit  of  power  will  be  one  erg  per  second.  As  this  unit  is 
inconveniently  small,  a  unit  ten  million  times  larger,  called 
the  Watt,  is  taken  as  a  practical  unit  of  power.  For  larger 
quantities  of  power  the  Kilowatt,  which  is  1000  watts,  is 
preferred.  One  horse-power,  which  by  definition  is  550 
foot-pounds  per  second,  is  equal  to  746  watts,  or  to  0'746 
kilowatt. 

Heat.  —  The  unit  of  heat,  the  calorie,  is  the  amount  of  heat 
required  to  warm  one  gramme  mass  of  water  one  degree 
(Centigrade) ;  and  the  dynamical  equivalent  of  this  amount 
of  heat  is  42  million  ergs,  which  is  known  as  Joule's  equiva- 
lent, as  expressed  in  C.G.S.  measure  (see  also  Art.  459). 


260         ELECTRICITY   AND   MAGNETISM     [PT.  n.  300,  301 

These  units  are  sometimes  called  "  absolute  "  unit;  the  term 
absolute,  introduced  by  Gauss,  meaning  that  they  are  independent 
of  the  size  of  any  particular  instrument,  or  of  the  value  of  grav- 
ity at  any  particular  place,  or  of  any  other  arbitrary  quantities 
than  the  three  standards  of  length,  mass,  and  time.  It  is,  how- 
ever, preferable  to  refer  to  them  by  the  more  appropriate  name  of 
"  C.G.S.  units,"  as  being  derived  from  the  centimetre,  the  gramme, 
and  the  second. 

300.  Electrical   Units.  —  There  are   two   systems  of    electrical 
units  derived  from  the  fundamental  "  C.G.S."  units,  one  set  being 
based  upon  the  force  exerted  between  two  quantities  of  electricity, 
and  the  other  upon  the  force  exerted  between  two  magnet  poles. 
The  former  set  are  termed  electrostatic  units,   the  latter  electro- 
magnetic units.     The  important  relation  between  the  two  sets  is 
explained  in  Chap.  V.,  Art.  386,  p.  347. 

301.  Electrostatic    Units.  —  No    special    names   have    been   as- 
signed to  the  electrostatic  units  of  Quantity,  Potential,  Capacity, 
etc.     The  reasons  for  adopting  the  following  values  as  units  are 
given  either  in  Chapter  I.  or  in  the  present  chapter. 

Unit  of  Quantity.  —  The  unit  of  quantity  is  that  quantity  of 
electricity  which,  when  placed  at  a  distance  of  one  cen- 
timetre (in  air)  from  a  similar  and  equal  quantity,  repels  it 
with  a  force  of  one  dyne  (Art.  279),  p.  241. 

Potential.  —  Potential  being  measured  by  work  done  in  moving 
a  unit  of  +  electricity  against  the  electric  forces,  the  unit 
of  potential  will  be  measured  by  the  number  of  ergs,  per 
unit  of  electricity. 

Unit  Difference  of  Potential.  —  Unit  difference  of  potential 
exists  between  two  points,  when  it  requires  the  expendi- 
ture of  one  erg  of  work  to  bring  a  -f-  unit  of  electricity 
from  one  point  to  the  other  against  the  electric  fore© 
(Art.  283). 

Unit  of  Capacity.  —  Unit  capacity  exists  between  two  conduc- 
tors if  the  transfer  of  one  unit  of  electricity  from  one  to  the 
other  produces  unit  difference  of  potential  between  them. 
An  isolated  sphere  of  one  centimetre  radius  possesses  unit 
capacity  (Art.  290),  p.  252. 

Specific  Inductive  Capacity,  or  Inductivity,  is  denned  in  Art.  315 
as  the  ratio  between  two  quantities  of  electricity.  The 
specific  inductive  capacity  of  the  air  is,  in  the  absence  of  any 
knowledge  of  its  absolute  value,  taken  as  unity. 

Electromotive  Intensity  or  Potential  Gradient  is  the  electric 
force  or  intensity  of  an  electric  field  at  any  point,  and  is 


CH.  iv.  302]  DIMENSIONS   OF  UNITS  261 

measured  by  the  force  which  it  exerts  on  a  unit  charge 
placed  at  that  point. 

It  may  be  convenient  here  to  append  the  rules  for  reduc- 
ing to  their  corresponding  values  in  terms  of  the  practi- 
cal (electro-magnetic)  units,  values  that  may  have  been 
expressed  in  terms  of  the  electrostatic  units,  as  follows  :  — 

Potential.     To  bring  to  volts  multiply  by  300. 

Capacity.      To  bring  to  microfarads  divide  by  900,000. 

Current.        To  bring  to  amperes  divide  by  3  X  109. 

Resistance.  To  bring  to  ohms  multiply  by  9  X  10n. 

Quantity.      To  bring  to  coulombs  divide  by  3  X  109. 
To  bring  coulombs  to  electrons,  multiply  by  8  X  1018. 
To  bring  electrostatic  units  of  quantity  to  electrons,  multiply  by 

3'35  X  10°. 

Example.  —  Suppose  two  equally  charged  spheres  whose  centres 
are  40  centimetres  apart  are  found  to  repel  one  another 
with  a  force  of  630  dynes  (  =  about  the  weight  of  10  grains). 
By  the  law  of  inverse  squares  we  find  that  the  charge  on 
each  is  1004  (electrostatic)  units.  Dividing  by  3  X  109  we 
find  that  this  amounts  to  0*0000003347  coulomb. 

302.  Dimensions  of  Units.  —  It  has  been  assumed  above 
that  a  velocity  can  be  expressed  in  centimetres  per  second ;  for 
velocity  is  rate  of  change  of  place,  and  it  is  clear  that  if  change 
of  place  may  be  measured  as  a  length  in  centimetres,  the  rate  of 
change  of  place  will  be  measured  by  the  number  of  centimetres 
through  which  the  body  moves  in  unit  of  time.  It  is  impossible, 
indeed,  to  express  a  velocity  without  regarding  it  as  the  quotient 
of  a  certain  number  of  units  of  length  divided  by  a  certain  number 

of  units   of   time.     In   other  words,   a  velocity  = =— ^ — :    or. 

a  time 

adopting  L  as  a  symbol  for  length,  and  T  as  a  symbol  for  time, 
V  =  L  -f-  T,  which  is  still  more  conveniently  written,  V  =  L  X  T"1. 
In  a  similar  way  acceleration  being  rate  of  change  of  velocity,  we 

have  A  =  -  =  -~>  =  -  =  L  x  T~2- 

T         TXT         T 

Now  these  physical  quantities,  "  velocity  "  and  "  acceleration," 
are  respectively  always  quantities  of  the  same  nature,  no  matter 
whether  the  centimetre,  or  the  inch,  or  the  mile,  be  taken  as  the 
unit  of  length,  or  the  second  or  any  other  interval  be  taken  as  the 
unit  of  time.  Hence  we  say  that  these  abstract  equations  express 


262 


ELECTRICITY   AND   MAGNETISM         [PT.  11.  303 


the  dimensions  of  those  quantities  with  respect  to  the  fundamental 
quantities  length  and  time.  A  little  consideration  will  show  that 
the  dimensions  of  the  various  units  mentioned  above  will  therefore 
be  as  given  in  the  table  following. 

The  dimensions  of  magnetic  units  are  given  in  the  Table  in 
Art.  383,  p.  344. 

303.    Scalar  and  Vector  Quantities.  —  Scalar  quantities  are  those 

which  can  be  completely  expressed  by  a  number  in  terms  of  a  unit, 

or  quantities  which  do  not  imply  direction.     Such  quantities  are  :  — 

time,     temperature,     numbers,     area,     volume,     work,     energy, 

resistance,  inductance,  capacity,  etc. 

Vector  quantities  are  those  which  express  a  direction  as  well  as 
a  numerical  value  of  their  magnitude  as  compared  with  a  unit. 
The  following  are  vector  quantities  :  — 

length,  velocity,  acceleration,  force,  momentum,  etc. 
TABLE  OF  DIMENSIONS  OF  UNITS 


UNITS 

DIMENSIONS 

(Fundamental) 

1 

Length 

L 

m 

Mass 

M 

t 

Time 

T 

(Derived) 

Area                              L  x  L 

L2 

Volume                         L  X  L  X  L 

L3 

V 

Velocity                        L  H-  T 

LT'1 

a 

Acceleration   =  velocity  -4-  time 

LT-2 

f 

Force               =      mass  X  acceleration    = 

MLT-2 

Work               =      force  X  length 

ML2T'2 

Power              =      work  -4-  time 

ML2T~3 

(Electrostatic) 

• 

Q 

Quantity         =  Vforce  X  (distance)2       = 

M*~L?T~lk 

i 
V 

Current           =  quantity  -4-  time 
Potential         =  work  -4-  quantity 

M^T-'AT* 

R 

Resistance      =  potential  -r-  current          = 

L^T1^"1 

C 

Capacity         =  quantity  -4-  potential        = 

LA;1 

k 

Sp.  Ind.  Capacity  =  quantity  -4-  another  quantity 

a  numeral 

F 

Electromotive  Intensity  =  force  -4-  quantity  = 

_^V 

CH.  iv.  304, 305]  ELECTROMETERS  263 

LESSON  XXII.  —  Electrometers 

304.  In   Lesson   II.  we   described   a   number   of   electro- 
scopes or  instruments  for  indicating  the  presence  and  sign 
of  a  charge  of  electricity ;  some  of  these  also  served  to  indicate 
roughly  the  amount  of  these  charges,  but  none  of  them  save 
the  torsion  balance  could  be  regarded  as  affording  an  accurate 
means  of  measuring  either  the  quantity  or  the  potential  of  a 
given  charge.     An  instrument  for  measuring  differences  of 
electrostatic  potential  is  termed  an  Electrometer.     Such  instru- 
ments can  also  be  used  to  measure  electric  quantity  indirectly, 
for  the  quantity  of  a  charge  can  be  ascertained  by  measuring 
the  potential  to  which  it  can  raise  a  conductor  of  known 
capacity.     The  earliest  electrometers  attempted  to  measure 
the  quantities  directly.     Lane  and  Snow  Harris  constructed 
"  Unit  Jars  "  or  small  Ley  den  jars,  which,  in  order  to  measure 
out  a  certain  quantity  of  electricity,  were  charged  and  dis- 
charged a  certain  number  of  times. 

305.  Repulsion    Electrometers.  —  The    torsion    balance, 
described  in  Art.  18,  measures  quantities  by  measuring  the 
forces  exerted  by  the  charges  given  to  the  fixed  and  movable 
balls.     It  can  only  be  applied  to  the  measurement  of  repelling 
forces,  for  the  equilibrium  is  unstable  in  the  case  of  a  force 
of  attraction. 

Beside  the  gold-leaf  and  other  electroscopes  described 
in  Lesson  II.,  there  exist  several  delicate  electrometers  based 
upon  the  principle  of  repulsion,  some  of  which  resemble  the 
torsion  balance  in  having  a  movable  arm  turning  about  a 
central  axis.  Amongst  these  are  the  electrometers  of  Dell- 
mann  and  of  Peltier.  In  the  latter  a  light  arm  of  aluminium, 
balanced  upon  a  point,  carries  also  a  small  magnet  to  direct 
it  in  the  magnetic  meridian.  A  fixed  arm,  in  metallic  contact 
with  the  movable  one,  also  lies  in  the  magnetic  meridian. 
A  charge  imparted  to  this  instrument  produces  a  repulsion 
between  the  fixed  and  movable  arms,  causing  an  angular 
deviation.  Here,  however,  the  force  is  measured  not  by 


264  ELECTRICITY   AND   MAGNETISM        [PT.  n.  306 

being  pitted  against  the  torsion  of  an  elastic  fibre,  or  against 
gravitation,  but  against  the  directive  magnetic  force  of  the 
earth  acting  on  the  small  needle.  Now  this  depends  on  the 
intensity  of  the  horizontal  component  of  the  earth's  magnet- 
ism at  the  place,  on  the  magnetic  moment  of  the  needle,  and 
on  the  sine  of  the  angle  of  its  deviation.  Hence,  to  obtain 
quantitative  values  for  the  readings  of  this  electrometer,  it 
is  necessary  to  make  preliminary  experiments  and  to  "  cali- 
brate "  the  degree-readings  of  the  deviation. 

306.  Attracted-Disk  Electrometers.  —  Snow  Harris  con- 
structed an  electrometer  by  measuring  the  attraction  between 
an  electrified  and  a  non-electrified  disk ;  and  the  instrument 
he  devised  may  be  roughly  described  as  a  balance  for  weigh- 
ing a  charge  of  electricity.  The  force  exerted  by  an  electrified 
point  falls  off  inversely  as  the  square  of  the  distance,  since 
the  lines  of  force  emanate  in  radial  lines.  But  in  the  case  of 
a  uniformly  electrified  plane  surface,  the  lines  of  force  are 
normal  to  the  surface,  and  parallel  to  one  another;  and 
the  force  is  independent  of  the  distance.  The  distribution 
over  a  small  sphere  nearly  fulfils  the  first  of  these  conditions. 
The  distribution  over  a  flat  disk  would  nearly  fulfil  the  latter 
condition,  were  it  not  for  the  perturbing  effect  of  the  edges 
of  the  disk  where  the  surface-density  is  much  greater  (see 
Art.  38). 

Lord  Kelvin  introduced  into  the  construction  of  attracted- 
disk  electrometers  the  employment  of  the  "  guard-plate  " 
and  the  providing  of  means  for  working  with  a  definite 
standard  of  potential.  It  would  be  beyond  the  scope  of 
these  lessons  to  give  a  complete  description  of  all  the  various 
forms  of  attracted-disk  electrometer ; 1  but  the  main  principles 
of  them  all  can  be  readily  explained. 

The  disk  C,  whose  attraction  is  to  be  measured,  is  sus- 
pended (Fig.  164)  within  a  fixed  guard-plate  B,  which  sur- 

1  For  these  the  student  is  referred  to  the  volume  of  Lord  Kelvin's  papers, 
"On  Electrostatics  and  Magnetism";  or  to  Professor  Andrew  Gray's 
Absolute  Measurements  in  Electricity  and  Magnetism. 


CH.  iv.  306]    ATTRACTED-DISK   ELECTROMETERS        265 

rounds  it  without  touching  it,  and  which  is  placed  in  metallic 
contact  with  it  by  a  fine  wire.  A  lever  L  supports  the  disk, 
and  is  furnished  with  a  counterpoise.  In  order  to  know 
whether  the  disk  is  precisely  level  with  the  lower  surface 
of  the  guard-plate  a  little  gauge  or  index  is  fixed  above,  and 
provided  with  a  lens  I  to  observe  its  indications.  Beneath 
the  disk  and  guard-plate  is  a  second  disk  A,  supported  on  an 
insulating  stand.  This  lower  disk  can  be  raised  or  lowered 
at  will  by  a  micrometer  screw,  great  care  being  taken  in  the 
mechanical  arrangements  that  it  shall  always  be  parallel  to 
the  plane  of  the  guard-plate.  Now,  since  the  disk  and  guard 


Fia.  164.  —  Attracted-Disk  Electrometer,  with  Guard-Plate. 

plate  are  in  metallic  connexion  with  one  another,  they  form 
virtually  part  of  one  surface,  and  as  the  irregularities  of 
distribution  occur  at  the  edges  of  the  surface,  the  distribu- 
tion over  the  area  of  the  disk  is  practically  uniform.  Any 
attraction  of  the  lower  plate  upon  the  disk  might  be  balanced 
either  by  increasing  the  weight  of  the  counterpoise,  or  by 
putting  a  torsion  on  the  aluminium  wire  which  serves  as  a 
fulcrum;  but  in  practice  it  is  found  most  convenient  to 
obtain  a  balance  by  altering  the  distance  of  the  lower  plate 
until  the  electric  force  of  attraction  exactly  balances  the  forces 
(whether  of  torsion  or  of  gravity  acting  on  the  counterpoise) 
which  tend  to  lift  the  disk  above  the  level  of  the  guard-plate. 


266  ELECTRICITY  AND  MAGNETISM      [PT.  IT.  306 

The  theory  of  the  instrument  is  simple  also.  Let  Vi 
represent  the  potential  of  the  movable  disk,  which  has  a 
positive  charge  of  surface-density  p,  and  let  V2  be  the  poten- 
tial of  the  fixed  plate,  upon  which  is  a  charge  of  surface- 
density  —  p.  The  difference  of  potential  Vi  —  ¥2  is  the 
work  which  would  have  to  be  done  upon  a  unit  of  positive 
charge  in  taking  it  from  V2  to  Vi.  Now  the  force  upon  such 
a  unit  placed  between  the  two  plates  would  be  (an  attraction 
of  2  irp  due  to  the  fixed  plate,  and  a  repulsion  of  2  irp  due  to  the 
movable  plate,  see  Art.  296)  altogether  4  irp,  and  if  the  dis- 
tance between  the  plates  were  D,  work  =  force  X  distance. 

Vi  -  V2  =  4  TrpD. 

If  S  is  the  area  of  the  movable  plate,  S/o  is  the  total  quantity 
of  electricity  on  it;  therefore  it  would  be  attracted  by  the 
fixed  plate  with  a  force  F  =  2-n-p  X  Sp.  From  this  we  get 


p  = 


Substituting  this  value  of  p  in  the  above,  equation,  we  get 


If  F  is  measured  in  dynes,  S  in  square  centimetres,  and 
D  in  centimetres,  the  potentials  will  be  in  absolute  electro- 
static units,  and  must  be  multiplied  by  300  to  bring  to 
volts  (see  Art.  301). 

From  this  we  gather  that,  if  the  force  F  remain  the  same 
throughout  the  experiments,  the  difference  of  potentials 
between  the  disks  will  be  simply  proportional  to  the  distance 
between  them  when  the  disk  is  in  level  equilibrium.  And 

lo      rp 

the  quantity  -v/ may  be  determined  once  for  all  as  a 

~    S 

"  constant  "  of  the  instrument. 

In  the  more  elaborate  forms  of  the  instrument,  such  as 
the  "  absolute  electrometer  "  and  the  "  portable  electrom- 
eter," the  disk  and  guard-plate  are  covered  with  a  metallic 


CH.  iv.  307]         QUADRANT   ELECTROMETER  267 

cage,  and  are  together  placed  in  communication  with  a 
condenser  to  keep  them  at  a  known  potential.  This  obviates 
having  to  make  measurements  with  zero  readings,  for  the 
differences  of  potential  will  now  be  proportional  to  differences 
of  micrometer  readings,  or, 


The  condenser  is  provided  in  these  instruments  with  a 
gauge,  itself  an  attracted  disk,  to  indicate  when  it  is  charged 
to  the  right  potential,  and  with  a  replenisher  to  increase  or 
decrease  the  charge,  the  replenisher  being  a  little  influence 
machine  (see  Art.  50). 

307.  The  Quadrant  Electrometer.  —  The  Quadrant  Elec- 
trometer of  Lord  Kelvin  is  an  example  of  a  different  class  of 
electrometers,  in  which  use  is  made  of  an 
auxiliary  charge  of  electricity  previously 
imparted  to  the  needle  of  the  instrument. 
The  needle,  which  consists  of  a  thin  flat 
piece  of  aluminium  hung  horizontally  by  a 
fibre  of  thin  wire,  charged,  say  positively, 
will  be  attracted  by  a  —  charge  but  re-  FIG.  165.— Needle  ana 
pelled  by  a  +  charge.  Such  attraction  or  %££££$£' 
repulsion  will  be  stronger  in  proportion  to 
these  charges,  and  in  proportion  to  the  charge  on  the  needle. 
Four  quadrant-pieces  (Fig.  165)  of  brass  are  fixed  horizontally 
below  the  needle  without  touching  it  or  one  another.  Oppo- 
site quadrants  are  joined  with  fine  wires.  If  quadrants 

1  and  3  are  ever  so  little  +  as  compared  with  quadrants 

2  and  4,  the  needle  will  turn  away  from  the  former  to  a 
position  more  nearly  over  the  latter. 

If  there  is  the  slightest  difference  of  potential  between 
the  pairs  of  quadrants,  the  needle,  which  is  held  in  its  zero 
position  by  the  elasticity  of  the  wire,  will  turn,  and  so  indicate 
the  difference  of  potential.  When  these  deflexions  are  small, 
the  scale  readings  will  be  very  nearly  proportional  to  the 


268 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  307 


difference  of  potential.  The  instrument  is  sufficiently 
delicate  to  show  a  difference  of  potential  between  the  quad- 
rants as  small  as  the  y1^  of  that  of  the  Daniell's  cell.  If  Vi  be 
the  potential  of  one  pair  of  quadrants,  V2  that  of  the  other 
pair,  and  V3  the  potential  of  the  needle,  the  force  tending  to 
turn  will  be  proportional  to  Vi  —  V2,  and  will  also  be  propor- 
tional to  the  difference  between  V3  and  the 
average  of  Yi  and  V2.  Or,  in  symbols, 


where  a  is  a  constant  depending  on  the 
construction  of  the  particular  instrument. 
Fig.  166  shows  a  very  simple  form  of 
the   Quadrant  Electrometer,  as  arranged 


FIG.  166.  —  Simple  Quadrant  Electrometer. 

for  qualitative  experiments.  The  four  quadrants  are  en- 
closed within  a  glass  case,  and  the  needle,  which  carries  a 
light  mirror  M  below  it,  is  suspended  from  a  torsion  head 
C  by  a  very  thin  metallic  wire  F.  It  is  electrified  to  a  certain 
potential  by  being  connected,  through  a  wire  attached  to  C, 
with  a  charged  Ley  den  jar  or  other  condenser.  In  order  to 
observe  the  minutest  motions  of  the  needle,  a  reading- 
telescope  and  scale  are  so  placed  that  the  observer  looking 
through  the  telescope  sees  an  image  of  the  zero  of  the  scale 
reflected  in  the  little  mirror.  The  wires  connecting  quadrants 
1  and  3,  2  and  4,  are  seen  above  the  top  of  the  case. 

For  very  exact  measurements  many  additional  refinements 
are  introduced  into  the  instrument.     Two  sets  of  quadrants 


CH.  iv.  308]         QUADRANT   ELECTROMETER  269 

are  employed,  an  upper  and  a  lower,  having  the  needle  be- 
tween them.  The  torsion  wire  is  replaced  by  a  delicate 
bifilar  suspension  (Art.  132).  To  keep  up  the  charge  of  the 
jar  a  "  replenisher  "  (Art.  50)  is  added;  and  an  "  attracted- 
disk,"  like  that  of  the  Absolute  Electrometer,  is  employed 
in  order  to  act  as  a  gauge  to  indicate  when  the  jar  is 
charged  to  the  right  potential.  In  these  forms  the  jar  consists 
of  a  glass  vessel  placed  below  the  quadrants,  coated  externally 
with  strips  of  tinfoil,  and  containing  strong  sulphuric  acid, 
which  serves  the  double  function  of  keeping  the  apparatus  dry 
by  absorbing  the  moisture  and  of  acting  as  an  internal  coat- 
ing for  the  jar.  It  is  also  more  usual  to  throw  a  spot  of  light 
from  a  lamp  upon  a  scale  by  means  of  the  little  mirror  (as 
described  in  the  case  of  the  Mirror  Galvanometer,  in  Art. 
228),  than  to  adopt  the  subjective  method  with  the  telescope, 
which  only  one  person  at  a  time  can  use.  When  the  instru- 
ment is  provided  with  replenisher  and  gauge,  the  measure- 
ments can  be  made  in  terms  of  absolute  units,  provided  the 
"  constant  "  of  the  particular  instrument  (depending  on 
the  suspension  of  the  needle,  size  and  position  of  needle  and 
quadrants,  potential  of  the  gauge,  etc.)  is  once  ascertained. 
In  a  recent  form,  due  to  Dolezalek,  the  sensitiveness  is  in- 
creased by  suspending  the  needle  by  a  quartz  fibre  as  thin  as 
•rfar  millimetre,  rendered  conductive  by  depositing  a  film  of 
silver  upon  it. 

308.  Use  of  Quadrant  Electrometer.  —  An  example  will  illus- 
trate the  mode  of  using  the  instrument.  It  is  known  that  when 
the  two  ends  of  a  thin  wire  are  kept  at  two  different  potentials  a 
current  flows  through  the  wire,  and  that  if  the  potential  is  meas- 
ured at  different  points  along  the  wire,  it  is  found  to  fall  off  in  a 
perfectly  uniform  manner  from  the  end  that  is  at  a  high  potential 
down  to  that  at  the  low  potential.  At  a  point  one  quarter  along 
the  potential  will  have  fallen  off  one  quarter  of  the  whole  difference. 
This  could  be  proved  by  joining  the  two  ends  of  the  wire  through 
which  the  current  was  flowing  to  the  terminals  of  the  Quadrant 
Electrometer,  when  one  pair  of  quadrants  would  be  at  a  high 
potential  and  the  other  at  a  low  potential.  The  needle  would  turn 
and  indicate  a  certain  deflexion.  Now,  disconnect  one  of  the  pairs 


270  ELECTRICITY   AND   MAGNETISM      [PT.  n.  309 

of  quadrants  from  the  low  potential  end  of  the  wire,  and  place 
them  in  communication  with  a  point  one  quarter  along  the  wire  from 
the  high  potential  end.  The  needle  will  at  once  indicate  that  the 
difference  of  potential  is  but  one  quarter  of  what  it  was  before. 

Often  the  Quadrant  Electrometer  is  employed  simply  as  a  very 
delicate  electroscope  in  systems  of  measurement  in  which  a  difference 
of  electric  potential  is  measured  by  being  balanced  against  an  equal 
and  opposite  difference  of  potential,  exact  balance  being  indicated 
by  there  being  no  deflexion  of  the  Electrometer  needle.  Such 
methods  of  experimenting  are  known  as  Null  Methods,  or  Zero 
Methods. 

309.  Electrostatic  Voltmeter.  —  We  have  seen  that  in 
the  quadrant  electrometer  it  is  necessary  to  give  the  needle 
a  high  initial  charge,  the  reason  being  that  if 
there  did  not  exist  between  the  quadrants 
and  the  needle  a  much  greater  difference 
of  potential  than  the  small  voltage  we  are 
measuring,  the  force  tending  to  turn  the 
needle  would  be  too  small  to  be  conven- 
iently observed.  Where,  however,  we  are 
dealing  with  high  differences  of  potential  a 
separately-charged  needle  is  not  requisite; 
we  may  simply  join  one  conductor  to  the 
FIG.  167.  —  Electro-  needle  and  the  other  to  a  set  of  quadrants, 

static  Voltmeter.         and    the    force    Qf    attraction>     wmch>     other 

things  being  equal,  increases  as  the  square  of  the  difference 
of  potential,  is  sufficiently  great  to  give  reliable  readings. 
This  is  known  as  the  idiostatic  method  of  using  the  instru- 
ment. 

A  front  view  of  the  instrument  as  commonly  used  to 
measure  differences  of  potential  of  1000  volts  or  more,  is 
shown  in  Fig.  167.  The  needle  NN  is  a  paddle-shaped  plate 
of  aluminium  supported  by  knife  edges  at  its  centre ;  its 
position  is  controlled  by  gravity,  little  weights  being  hung  on 
a  projection  at  its  lower  end.  The  quadrants  Q  are  both 
behind  and  in  front  of  it,  and  so  placed  that  when  a  differ- 
ence of  potential  exists  between  the  needle  and  them,  the 


cs.  iv.  310]       ELECTROSTATIC   VOLTMETER 


271 


FIG.  168.  —  Multi- 
cellular  Electro- 
static Voltmeter. 


needle  is  deflected  from  its  normal  position  and  moves  its 

pointer  over  a  graduated  scale. 

It  will   be   seen   that  it   does    not   matter   whether   the 

needle  is  positively  charged  and  the  quadrants  negatively 

charged  or  vice  versa ;  an  attraction  between 

the  two  will  always  take  place,  so  a  deflexion 

will  be  given  even  when  the    difference   of 

potential  is  rapidly  alternating.     This  prop- 
erty of  the  instrument  makes  it  exceedingly 

useful  for  the  measurement  of  voltage  when 

alternating  currents  are  used. 

Another  advantage  of  this  instrument  over 

the   high-resistance  galvanometers   that  are 

used  as  voltmeters  is,  that  it  does  not  take 

any  current,  and  consequently  it  does  not 

waste  any  power. 

In  order  to  make  the  electrostatic  volt- 
meter sufficiently  delicate  to  measure  down  to  100  volts  or 

so,  a  number  of  needles  or  vanes  are  placed  horizontally  one 

above  the  other  on  a  vertical  aluminium  wire,  and  attracted 
by  a  tier  of  quadrants  symmetrically 
placed  on  each  side ;  this  instrument  is 
Lord  Kelvin's  multicellular  voltmeter.  It 
is  shown  in  elevation  and  plan  in  Fig.  168. 
310.  Wilson's  Electrometer.  — In  this 
instrument  (Fig.  169)  a  single  gold  leaf 
is  suspended  in  front  of  a  vertical  metal 
strip  fixed  at  the  top  in  an  insulating  bead 
of  sulphur  or  to  a  piece  of  fused  quartz. 
To  charge  it,  a  crooked  wire  which  comes 
in  through  an  ebonite  plug  at  the  top  is 
turned  to  touch  the  metal  support ;  then 
the  charge  is  imparted,  and  the  charging 
wire  turned  out  of  contact  leaving  the 

gold  leaf   diverging,    by    repulsion    from    the    fixed    strip. 

The  deflexion  of  the  gold  leaf  is  observed  by  a  microscope 


FIG.   169.  —  Wilson's 
Electrometer. 


272 


ELECTRICITY  AND   MAGNETISM    [PT.  n.  311-314 


through  a  glass  window  in  the  case,  or  is  projected  upon  a 
scale. 

311.  Dry-Pile   Electrometer.  —  The    principle    of    sym- 
metry observed  in  the  Quadrant  Electrometer  was  previ- 
ously employed  in  the  Electroscope  of  Bohnenberger  —  a 
much  less  accurate  instrument  —  in  which  the  charge  to  be 
examined  was  imparted  to  a  single  gold  leaf,  placed  sym- 
metrically between  the  poles  of  a  dry-pile  (Art.  203),  toward 
one  or  other  pole  of  which  the  leaf  was  attracted.     Fechner 
modified  the  instrument  by  connecting  the  +  pole  of  the  dry- 
pile  with  a  gold  leaf  hanging  between  two  metal  disks,  from 
the  more  +  of  which  it  was  repelled.     The  inconsistency  of 
dry-piles  as  sources  of  electrification  led  Hankel  to  substitute 
a  battery  of  a  very  large  number  of  small  DanielFs  cells. 

312.  Capillary  Electrometers.  —  The  Capillary  Electrom- 
eter of  Lippmann  was  described  in  Art.  269. 


LESSON  XXIII.  —  Dielectric  Capacity,  etc. 

313.  A  Ley  den  jar  or  other  condenser  may  be  regarded  as 
a  conductor  in  which  (owing  to  the  particular  device  of 
bringing  near  together  the  two  oppositely-charged  surfaces) 
the  conducting  surface  can  be  made 
to  hold  a  very  large  charge  without 
its  potential  (whether  +  or  — )  rising 
very  high.  The  capacity  of  a  con- 
denser, like  that  of  a  simple  con- 
ductor, will  be  measured  (see  Art. 
289)  by  the  quantity  of  electricity 
required  to  produce  unit  rise  of 
potential. 

314.  Theory  of  Spherical  Conden- 
ser. —  Suppose  a  Leyden  jar  made 
of  two  concentric  metal  spheres,  one 
inside  the  other,  the  space  between  them  being  filled  by  air. 
The  inner  one,  A,  will  represent  the  interior  coating  of  tin- 


FIG.   170.  —  Spherical  Con- 
denser. 


CH.  iv.  314]  CAPACITY   OF   CONDENSERS  273 

foil,  and  the  outer  sphere,  B  (Fig.  170)  will  represent  the 
exterior  coating.  Let  the  radii  of  these  spheres  be  r  and  r' 
respectively.  Suppose  a  charge  of  Q  units  to  be  imparted 
to  A ;  it  will  induce  on  the  inner  side  of  B  an  equal  negative 
charge  -  Q,  and  to  the  outer  side  of  B  a  charge  +  Q  will  be 
repelled.  This  latter  is  removed  by  contact  with  "  earth  " 
and  need  be  no  further  considered.  The  potential l  at  the 
centre  M,  calculated  by  the  rule  given  in  Art.  280,  will  be 


At  a  point  N,  outside  the  outer  sphere  and  quite  near  to  it, 
the  potential  will  be  the  same  as  if  these  two  charges  -f-  Q 
and  —  Q,  were  both  concentrated  at  M.  Hence 


So  then  the  difference  of  potentials  will  be 


TTf 

whence 


VM-VN      r'-r 
But  by  Art.  289  the  capacity  C  =  ^~^> 

therefore  C  =    _!Zl_. 
r'-r 

We  see  from  this  formula  that  the  capacity  of  the  con- 
denser is  proportional  to  the  size  of  the  metal  globes,  and 
that  if  the  insulating  layer  is  very  thin,  —  that  is,  if  r  be  very 
nearly  as  great  as  r',  r'  —  r  will  become  very  small,  and  the 

value  of  the  expression  — — —  will  become  very  great ;  which 


proves  the  statement  that  the  capacity  of  a  condenser  de- 

1  As  there  is  no  electric  force  within  a  closed  conductor,  the  potential 
at  the  middle  is  just  the  same  as  at  any  other  point  inside. 
T    . 


274  ELECTRICITY   AND   MAGNETISM     [PT.  n.  315 

pends  upon  the  thinness  of  the  layer  of  dielectric.  If  r'  is 
very  great  compared  with  r,  the  expression  for  the  capacity 
becomes  equal  simply  to  r,  that  of  the  inner  sphere  when  iso- 
lated. 

315.  Specific  Inductive  Capacity.  —  Cavendish  was  the 
first  to  discover  that  the  capacity  of  a  condenser  depended 
not  on  its  actual  dimensions  only,  but  upon  the  inductivity 
of  the  material  used  as  the  dielectric  between  the  two  surfaces. 
If  two  condensers  (of  any  of  the  forms  to  be  described)  be 
made  of  exactly  the  same  size,  and  in  one  of  them  the  dielec- 
tric be  a  layer  of  air,  and  in  the  other  a  layer  of  some  other 
insulating  substance,  it  is  found  that  equal  quantities  of  elec- 
tricity imparted  to  them  do  not  produce  equal  differences  of 
potentials  ;  or,  in  other  words,  it  is  found  that  they  have  not 
the  same  capacity.  If  the  dielectric  be  mica,  for  example,  it 
is  found  that  the  capacity  is  about  six  times  as  great;  for 
mica  possesses  a  high  inductivity  and  allows  electrostatic 
influence  to  act  across  it  six  times  as  well  as  air  does.  The 
name  inductivity,  or  specific  inductive  capacity,1  or  dielectric 
capacity,  is  given  to  the  ratio  between  the  capacities  of  two 
condensers  equal  in  size,  one  of  them  filled  with  the  specified 
dielectric,  the  other  being  an  air  condenser.  The  inductiv- 
ity of  dry  air  at  the  temperature  0°  C.,  and  pressure  76  cen- 
timeters, is  taken  as  the  standard  ;  and,  in  the  absence  of  any 
known  way  of  finding  its  absolute  value,  is  reckoned  as  unity. 
The  symbol  k  is  used  to  denote  the  inductivity  of  any  ma- 
terial. 

Cavendish,  about  the  year  1775,  measured  the  inductivity 
of  glass,  bees-wax,  and  other  substances,  by  forming  them 
into  condensers  between  two  circular  metal  plates,  the  ca- 
pacity of  these  condensers  being  compared  with  that  of  an 
air  condenser  (resembling  Fig.  41)  and  with  other  con- 
densers which  he  called  "  trial-plates."  He  even  went  so 

1  This  name  is  not  a  very  happy  one,  —  inductivity  is  better,  and  is  the 
analogous  term,  for  dielectrics,  to  the  term  "conductivity"  used  for  con- 
ductors. 


CH.  iv.  316] 


INDUCTIVITY 


275 


far  as  to  compare  the  capacities  of  these  "  trial-plates  "  with 
that  of  an  isolated  sphere  of  Yl\  inches  diameter  hung  up 
in  a  room. 

316.  Faraday's  Experiments.  —  In  1837  Faraday,  who 
did  not  know  of  the  then  unpublished  researches  of 
Cavendish,  independently  discovered 
inductivity,  and  measured  its  value 
for  several  substances,  using  for  this 
purpose  two  condensers  of  the  form 
shown  in  Fig.  171.  Each  consisted  of 
a  brass  ball  A  enclosed  inside  a  hollow 
sphere  of  brass  B,  and  insulated  by  a 
long  plug  of  shellac,  up  which  passed  a 
wire  terminating  in  a  knob  a.  The 
outer  sphere  consisted  of  two  parts 
which  could  be  separated  from  each 
other  in  order  to  fill  the  hollow  space 
with  any  desired  material :  the  experi- 
mental process  then  was  to  compare 
their  capacities  when  one  was  filled 
with  the  substance  to  be  examined, 
the  other  containing  only  dry  air. 
One  of  the  condensers  was  charged 
with  electricity.  It  was  then  made  FlG-  17i1c'aj~c 
to  share  its  charge  with  the  other  con- 
denser, by  putting  the  two  inner  coatings  into  metallic 
communication  with  one  another;  the  outer  coatings  also 
being  in  communication  with  one  another.  If  their  ca- 
pacities were  equal  they  would  share  the  charge  equally, 
and  the  potential  after  contact  would  be  just  half  what 
it  was  in  the  charged  condenser  before  contact.  If  the 
capacity  of  one  was  greater  than  the  other  the  final  po- 
tential would  not  be  exactly  half  the  original  potential,, 
because  they  would  not  share  the  charge  equally,  but  in 
proportion  to  their  capacities.  The  potentials  of  the  charges 
were  measured  before  and  after  contact  by  means  of  a 


276  ELECTRICITY   AND   MAGNETISM     [PT.  n.  317 

torsion  balance.1  Faraday's  results  showed  the  following 
values:  Sulphur,  2-26;  shellac,  2-0;  glass,  1-76  or  more. 

317.  Modern  Measurements.  —  Gibson  and  Barclay 
measured  the  inductivity  of  paraffin  wax  by  comparing 
the  capacity  of  an  air  condenser  with  one  of  paraffin  by 
means  of  an  arrangement  of  sliding  condensers,  using  a 
sensitive  quadrant  electrometer  to  adjust  the  capacity  of 
the  condensers  exactly  to  equality.  Hopkinson  examined 
the  inductivity  of  glass  of  various  kinds,  using  a  constant 
battery  to  produce  the  required  difference  of  potentials, 
and  a  condenser  provided  with  a  guard-ring  for  a  purpose 
similar  to  that  of  the  guard-ring  in  absolute  electrometers. 
Gordon  made  a  large  number  of  observations,  using  a  deli- 
cate apparatus  known  as  a  statical  "  inductivity  balance," 
which  is  a  complicated  condenser,  so  arranged  in  connexion 
with  a  quadrant  electrometer  that  when  the  capacities  of 
the  separate  parts  are  adjusted  to  equality  there  shall  be  no 
deflexion  in  the  electrometer,  whatever  be  the  amount  or 
sign  of  the  electrification  at  the  moment.  This  arrangement, 
when  employed  in  conjunction  with  an  induction  coil  (Fig. 
150)  and  a  rapid  commutator,  admits  of  the  inductive  capac- 
ity being  measured  when  the  duration  of  the  actual  charge 
is  only  very  small,  the  electrification  being  reversed  12,000 
times  per  second.  Such  an  instrument,  therefore,  over- 
comes one  great  difficulty  besetting  these  measurements, 
namely,  that  owing  to  the  apparent  absorption  of  part  of  the 
charge  by  the  dielectric  (as  mentioned  in  Art.  62),  the  capac- 

1  The  value  of  the  dielectric  capacity  k  could  then  be  calculated  as  fol- 
lows :  — 

Q  =  VC  =  V'C  +  V'Cfc 

(where  C  is  the  capacity  of  the  first  apparatus  and  V  is  potential,  and  V 
the  potential  after  communication  with  the  second  apparatus,  whose  capacity 
is  Cfc) :  hence 

V  =  V'(l  +  k), 

v-v 

and  k  =  -7-. 


CH.  iv.  318] 


INDUCTIVITY   OF   SOLIDS 


277 


ity  of  the  substance,  when  measured  slowly,  is  different  from 
its  "  instantaneous  "  capacity.  This  electric  absorption  is 
discussed  further  in  Art.  319.  For  this  reason  the  values  as- 
signed by  different  observers  for  the  inductivity  of  various 
substances  differ  to  a  most  perplexing  degree,  especially  in 
the  case  of  the  less  perfect  insulators.  The  following  table 
summarizes  the  facts  :  — 


Air 
Glass 
Ebonite    . 
Gutta-percha    . 
India-rubber     . 
Paraffin  (solid) 
Shellac      . 
Sulphur    . 
Mica 


1-00 

3-013  to  3'258 

2-284 

2-462 

2-220  to  2-497 

1-9936 

2-74 

2-58 

5'5  to  8 


Hopkinson,  whose  method  was  a  "  slow  "  one,  found 
for  glass  much  higher  inductivities,  ranging  from  6-5  to 
10-1,  the  denser  kinds  having  higher  inductivity.  Caven- 
dish observed  that  the  apparent  capacity  of  glass  became 
much  greater  at  those  temperatures  at  which  it  begins  to 
conduct  electricity.  Boltzmann  found  that  in  the  case  of  two 
crystalline  substances,  Iceland  spar  and  sulphur,  the  induc- 
tivity is  different  in  different  directions,  according  to  their 
position  with  respect  to  the  axes  of  crystallization. 

318.  Inductivity  of  Liquids  and  Gases.  —  The  inductivity 
of  liquids  also  has  specific  values,  as  follows :  — 


Pure  Water 
Aniline 
Turpentine 
Petroleum 
Bisulphide  of  Carbon 


81-07 
7-30 
2-16 

2-03  to  2-07 
1-81 


Gases  have  inductivities  which  depend  on  the  pressure 
at  which  they  are  used.  If  the  inductivity  of  vacuum  is 
taken  as  unity  that  of  air  is  slightly  higher ;  the  values  for 
various  gases  being  found  as  follows  :  — 


278 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  319 


Air 

Ammonia 
Carbon  monoxide 
Carbon  dioxide 
Ethylene 
Helium 
Hydrogen 
Nitrogen 
Nitrous  oxide 
Sulphur  dioxide 


1-000586 

T00718 

1-000695 

1-000985 

1-00146 

1-000074 

1-000264 

1-000581 

1-00099 

1-00905 


The  effect  of  using  instead  of  air  a  medium  of  higher 
inductivity  k  is  to  change  the  forces  exerted  between  charged 
bodies.  For  given  fixed  charges  the  forces  vary  inversely 
as  k ;  while  for  given  differences  of  potential  between  the 
bodies  the  forces  vary  directly  as  k. 

319.  Mechanical  Effects  of  Dielectric  Stress.  —  That 
different  insulating  substances  have  inductivity  sufficiently 
disproves  the  idea  that  influence  is  merely  an  "  action  at  a 
distance,"  for  it  is  evident  that  the  dielectric  medium  is  it- 
self concerned  in  the  propagation  of  influence,  and  that 
some  media  allow  influence  to  take  place  across  them  better 
than  others.  The  existence  of  a  residual  charge  (Art.  62) 
can  be  explained  either  on  the  supposition  that  the  dielectric 
is  composed  of  heterogeneous  particles  which  have  unequal 
conducting  powers,  as  Maxwell  has  suggested,  or  on  the  hy- 
pothesis that  the  molecules  are  actually  subjected  to  a  strain 
from  which,  especially  if  the  stress  be  long  continued,  they 
do  not  recover  all  at  once.  Kohlrausch  and  others  have 
pointed  out  the  analogy  between  this  phenomenon  and  that 
of  the  "  elastic  recovery  "  of  solid  bodies  after  being  subjected 
to  a  bending  or  a  twisting  strain.  A  fibre  of  glass,  for  ex'ample, 
twisted  by  a  certain  force,  flies  back  when  released  to  almost 
its  original  position,  a  slight  sub-permanent  set  remains, 
from  which,  however,  it  slowly  recovers  itself,  the  rate  of  its 
recovery  depending  upon  the  amount  and  duration  of  the 
original  twisting  strain.  A  quartz  fibre  never  shows  any  sub- 
permanent  set.  Hopkinson  has  shown  that  it  is  possible  to 
superpose  several  residual  charges,  even  charges  of  opposite 


CH.  iv.  319]  DIELECTRIC   STRESS  279 

signs,  which  apparently  "  soak  out  "  as  the  strained  material 
gradually  recovers  itself.  Perry  and  Ayrton  also  investi- 
gated the  question,  and  have  shown  that  the  polarization 
charges  in  voltameters  exhibit  a  similar  recovery.1  Air  con- 
densers exhibit  no  residual  charges.  Nor  do  plates  of  quartz 
cut  from  homogeneous  crystal. 

When  a  condenser  is  discharged  a  sound  is  often  heard. 
This  was  noticed  by  Lord  Kelvin  in  the  case  of  air  con- 
densers; Varley  and  Dolbear  constructed  telephones  in 
which  the  rapid  charge  and  discharge  of  a  condenser  gave 
rise  to  musical  tones  and  to  articulate  speech. 

As  to  the  precise  nature  of  the  molecular  or  mechanical 
operations  in  the  dielectric  when  thus  subjected  to  the 
stress  of  electrostatic  induction,  nothing  is  known.  One 
pregnant  experiment  of  Faraday  is  of  great  importance, 
by  showing  that  influence  is,  as  he  expressed  it,  "  an  action 
of  contiguous  particles."  In  a  glass  trough  (Fig.  172)  is 
placed  some  oil  of  turpentine,  in  which  are  put  some  fibres 
of  dry  silk  cut  into  small  bits.  Two  wires  pass  into  the  liquid, 
one  of  which  is  joined  to  earth,  the  other  being  put  into 
connexion  with  the  collector  of  an  electrical  machine.  The 
bits  of  silk  come  from  all  parts  of  the  liquid  and  form  a  quiver- 
ing chain  of  particles  from 
wire  to  wire,  showing  the 
electric  lines  of  force. 
They  at  once  disperse  if 
the  electric  discharge  is 

StODDed.  FaradaV         re-     FlG-  172-  ~~  Faraday's  Experiment  on  Action 

j     ,      ,  .  ..  of  the  Dielectric. 

garded  this  as  typical  of 

the  internal  actions  in  every  case  of  influence  across  a  dielec- 
tric, the  particles  of  which  he  supposed  to  be  "  polarized," 

1  It  would  appear,  therefore,  probable  that  Maxwell's  suggestion  of 
heterogeneity  of  structure,  as  leading  to  residual  electrification  at  the 
bounding  surface  of  the  particles  whose  electric  conductivities  differ,  is  the 
true  explanation  of  the  "residual"  charge.  The  phenomenon  of  elastic 
recovery  may  itself  be  due  to  heterogeneity  of  structure.  Glass  itself  is  a 
mixture  of  different  silicates. 


280         ELECTRICITY   AND   MAGNETISM     [PT.  n.  320,  321 

that  is,  to  be  turned  into  definite  positions,  each  particle 
having  a  positive  and  a  negative  end.  The  student  will  per- 
ceive an  obvious  analogy,  therefore,  between  the  condition 
of  the  particles  of  a  dielectric  across  which  influence  is  taking 
place,  and  the  molecules  of  a  piece  of  iron  or  steel  when  sub- 
jected to  magnetizing  forces.  Instead  of  silk,  crystals  of 
sulphate  of  quinine  may  be  used  in  specially  dried  benzol. 
Or  finely  divided  sulphide  of  antimony  may  be  strewn  on 
the  bottom  of  a  glass  dish  and  covered  with  a  layer  of  petro- 
leum, to  show  the  electric  lines  of  force. 

Werner  Siemens  showed  that  the  glass  of  a  Ley  den  jar 
is  sensibly  warmed  after  being  several  times  rapidly  charged 
and  discharged.  This  obviously  implies  that  molecular 
movement  accompanies  the  changes  of  dielectric  stress. 
The  phenomenon  is  called  dielectric  hysteresis. 

320.  Electric    Expansion.  —  Fontana    noticed    that    the 
internal  volume  of  a  Ley  den  jar  increased  when  it  was 
charged.     Priestly  and  Volta  sought  to  explain  this  by  sug- 
gesting that  the  attraction  between  the  two  charged  surfaces 
compressed  the  glass  and   caused  it  to  expand  laterally. 
Duter  showed  that  the  amount  of  apparent  expansion  was 
inversely  proportional  to  the  thickness  of  the  glass,  and  varied 
as  the  .square  of  the  potential  difference.     Quincke  has  ob- 
served that  an  apparent  contraction  is  shown  by  resins  and 
oily  bodies  under  electrostatic  stress. 

321.  Submarine   Cables   as   Condensers.  —  A  submarine 
telegraph  cable  may  act  as  a  condenser,  the  ocean  forming 
the  outer  coating,  the  internal  wire  the  inner  coating,  while 
the  insulating  layers   of  gutta-percha   serve   as  dielectric. 
When  one  end  of  a  submerged  cable  is  connected  to,  say, 
the  +  pole  of  a  powerful  battery,  electricity  flows  into  it. 
Before  any  signal  can  be  received  at  the  other  end,  enough 
electricity   must    flow   in   to   charge   the   cable  to   a   con- 
siderable potential,  an  operation  which  may  in  the  case  of 
long  cables  require  some  seconds.     Faraday  predicted  that 
this  retardation  would  occur.     It  is,  in  actual  fact,  a  serious 


CH.  iv.  322] 


CABLES  AS   CONDENSERS 


281 


obstacle  to  rapid  signalling  through  Atlantic  and  other 
cables.  Fleeming  Jenkin  devised  the  following  experimental 
demonstration  of  the  matter.  Let  a  mile  of  insulated  cable 
wire  be  coiled  up  in  a  tub  of  water  (Fig.  173),  one  end  N  being 
insulated.  The  other  end  is  joined  up  through  a  long-coil 
galvanometer  G  to  the  -f  pole  of  a  large  battery  whose  — 
pole  is  joined  by  a  wire  to  the  water  in  the  tub.  Directly 
this  is  done,  the  needle  of  the  galvanometer  will  show  a  violent 
deflexion,  electricity  rushing  through  it  into  the  interior  of  the 
cable,  and  a  —  charge  being  accumulated  on  the  outside  of  it 


FIG.  173.  —  Submarine  Cable  acts  as  a  Condenser. 

where  the  water  touches  the  gutta-percha.  For  perhaps 
an  hour  the  flow  will  go  on,  though  diminishing,  until  the 
cable  is  fully  charged.  Now  remove  the  battery,  and  in- 
stead join  up  a  and  6  by  a  wire ;  the  charge  in  the  cable  will 
rush  out  through  the  galvanometer,  which  will  show  an 
opposite  deflexion,  and  the  residual  charge  will  continue 
"  soaking  out  "  for  a  long  time. 

Long  land-lines  carried  overhead  also  possess  a  measure- 
able  capacity,  and  tend  to  retard  the  signals. 

322.  Condensers.  —  To  obviate  this  retardation  and  in- 
crease the  speed  of  signalling  in  cables  l  several  devices  are 
adopted.  Very  delicate  receiving  instruments  are  used, 
requiring  only  a  feeble  current ;  for  with  the  feebler  batteries 
the  actual  charge  given  to  the  cable  is  less.  In  some  cases 

1  The  capacity  of  the  "Direct"  Atlantic  cable  from  Ballinskelligs  (Ireland) 
to  Nova  Scotia  is  992  microfarads. 


282  ELECTRICITY   AND   MAGNETISM     [PT.  n.  323 

a  key  is  employed  which,  after  every  signal,  immediately 
sends  into  the  cable  a  charge  of  opposite  sign,  to  sweep  out, 
as  it  were,  the  charge  left  behind.  Often  a  condenser  of  sev- 
eral microfarads'  capacity  is  interposed  in  the  circuit  at  each 
end  of  the  cable  to  curb  the  signal,  or  make  it  shorter  and 
sharper,  and  by  its  reaction  assist  the  discharge.  In  duplex 
signalling  (Art.  586)  the  resistance  and  electrostatic  capacity 
of  the  cable  have  to  be  met  by  balancing  against  them  an 
"  artificial  cable  "  consisting  of  a  wire  of  equal  resistance, 
combined  with  a  condenser  of  equal  capacity.  Messrs. 
Muirhead  constructed  for  duplexing  the  Atlantic  cable  a 
condenser  containing  100,000  square  feet  (over  two  acres  of 
surface)  of  tinfoil.  Condensers  are  also  occasionally  used  in 
telegraph  lines  in  single  working  to  obviate  disturbances 
from  earth  currents.  They  are  constructed  by  placing  sheets 
of  tinfoil  between  sheets  of  mica  or  of  paraffined  paper, 
alternate  sheets  of  foil  being  connected  together.  The  paper 
is  the  finest  bank-wove,  carefully  selected  to  be  free  from  mi- 
nute holes.  Two  thicknesses,  drawn  through  a  bath  of  the 
purest  paraffin  wax  heated  till  it  melts,  are  laid  between  each 
foil  and  the  next;  care  being  taken  to  exclude  air  bubbles. 
When  a  sufficient  number  have  been  assembled  hot  they  are 
put  under  pressure  to  cool,  and  afterwards  adjusted.  Small 
condensers  of  similar  construction  are 
used  in  connexion  with  induction  coils 
(Fig.  150). 

323.    Standard    Condensers.  —  Elec- 
tricians adopt  a  unit  of  capacity,  termed 
one  farad,  based  on  the  system  of  elec- 
tromagnetic units.     A  condenser  of  one 
FIG.  174.  —  standard  con-    farad   capacity  would   be  raised  to  a 

denser  (^  microjarad).  ^      * 

potential  of  one  volt  by  a  charge  of  one 
coulomb  of  electricity.1  In  practice  such  a  condenser  would 
be  too  enormous  to  be  constructed ;  the  earth  itself,  as  an 
isolated  sphere,  has  a  capacity  of  only  TT£O~O  °f  a  farad. 

1  See  list  of  Practical  Electromagnetic  Units,  Art.  381. 


CH.  iv.  324,  325]  CONDENSERS  283 

As  a  practical  unit  of  capacity  the  microfarad,  or  one  millionth 
of  a  farad,  has  therefore  been  chosen;  a  capacity  about 
equal  to  that  of  three  miles  of  an  Atlantic  cable.  Condensers 
of  only  |  microfarad  are  about  equal  in  capacity  to  one 
nautical  mile  of  cable.  They  contain  about  1200  square 
inches  of  foil.  The  dielectric  in  them  is  usually  mica,  in  thin 
sheets.  Their  general  form  is  shown  in  Fig.  174.  The  two 
brass  pieces  upon  the  ebonite  top  are  connected  respectively 
with  the  two  series  of  alternate  sheets  of  tinfoil.  The  plug 
between  them  serves  to  keep  the  condenser  discharged  when 
not  in  use. 

Methods  of  measuring  the  capacity  of  a  condenser  are  given 
in  Art.  451,  p.  430. 

324.  Modern   Commercial   Condensers.  —  For  telegraph 
and  telephone  work  Mansbridge  has  devised  condensers  con- 
sisting of  long  slips  of  thin  paper  coated  on  one  side  with  tin 
powder  which  has  been  burnished  on  to  the  strip.     Each  con- 
denser is  formed  of  two  such  strips  rolled  up,  with  a  blank 
strip  of  thin  paper  between  them,  into  cylindrical  form. 
If  the  total  thickness  of  paper  between  the  foils  is  0-004  of  an 
inch,  the  two  coated  surfaces  will  be  about  6J  square  feet 
each,  in  a  condenser  of  1  microfarad  capacity.     Moscicki's 
high-voltage  jar  is  described  in  Art.  64. 

325.  Formulas  for  Capacities  of  Conductors  and  Condens- 
ers. —  The  following  formulae  give  the  capacity  of  condens- 
ers of  all  ordinary  forms,  in  electrostatic  units :  — 

Sphere:   (radius  =  r.     See  Art.  290),  if  in  air, 

C  =  r; 
or,  if  in  a  medium  of  inductivity  fc, 

C  =  kr. 
Two  Concentric  Spheres:  (radii  r  and  r'), 

r'  -  r' 


284  ELECTRICITY   AND   MAGNETISM     [PT.  n.  326 

Cylinder:    (length  =  I,  radius  =  r), 
C  =  fc— ^— ,• 


Two  Concentric  Cylinders:  (length  =  I,  internal  radius 
=  r,  external  radius  =  r'), 


2  logc- 
r 

Circular  Disk:    (radius  =  r,  thickness  negligible), 
C  =  2  7r/b/r. 

Two  Circular  Disks  :  (like  air  condenser,  Art.  57,  radii 
=  r,  surface  =  S,  thickness  of  dielectric  =  b  ;  provided 
r  is  very  great  relatively  to  6, 

C  =  ArV46, 
or  C  =  &S/4  irb. 

The  latter  formula  applies  to  any  two  parallel  disks  of  sur- 
face S,  whether  circular  or  otherwise,  provided  they  are  large  as 
compared  with  the  distance  6  between  them.  Tq  calculate 
down  to  microfarads,  the  numbers  given  by  any  of  the  above 
must  be  divided  by  900,000. 

326.  Energy  of  Discharge  of  Leyden  Jar  or  Condenser.  — 
It  follows  from  the  definition  of  potential,  given  in  Art.  280, 
that  in  bringing  up  one  +  unit  of  electricity  to  the  potential  V, 
the  work  done  is  V  ergs.  This  assumes,  however,  that  the  total 
potential  V  is  not  thereby  raised,  and  on  this  assumption  the 
work  l  done  in  bringing  up  Q  units  would  be  QV  ergs.  If, 
however,  the  potential  is  nothing  to  begin  with,  and  is  raised 
to  V  by  the  charge  Q,  the  average  potential  during  the  opera- 
tion is  only  J  V  ;  hence  the  total  work  done  in  bringing  up 
the  charge  Q  from  zero  potential  to  potential  V  is  J  QV  ergs. 
Now,  according  to  the  principle  of  the  conservation  of  energy, 

1  If  Q  is  given  in  coulombs  and  V  in  volts,  the  work  will  be  expressed  not 
in  ergs  but  in  joules  (Art.  381). 


CH.  iv.  327, 328]      CAPACITIES    IN    PARALLEL  285 

the  work  done  in  charging  a  jar  or  condenser  with  electricity 
is  equal  to  the  work  which  could  be  done  by  that  quantity  of 
electricity  when  the  jar  is  discharged.  Hence  J  QV  repre- 
sents also  the  energy  of  the  discharge. 

Since  Q  =  VC,  it  follows  that  we  may  write  \  QV  in  the 
form  \  Q2  -f-  C.  That  is  to  say,  if  a  condenser  of  capacity  C 
is  charged  by  having  a  charge  Q  imparted  to  it,  the  energy  of 
the  charge  is  proportional  directly  to  the  square  of  the  quan- 
tity, and  inversely  to  the  capacity  of  the  condenser. 

327.  Symbol   for    Condenser.  —  In   diagrams   of   electric 
circuits   electricians   use   as   symbols   for   condensers   those 
given  in  Fig.  175.         The  ori-  |— 
gin  of  these  symbols  is  the  al-     /^ .  .     ^        X'GSSpv 
ternate  layers  of  tinfoil.     The    '                     /  N 
symbol  on  the  right  suggests  six     FlG- 175-  -  Symbo1  for  Condensers. 
layers  of  foil,  of  which  the  first,  third,  and  fifth  are  joined 
together,  and  the  second,  fourth,  and  sixth  are  also  joined 
together. 

328.  Capacities  joined  in   Parallel.  —  To  join  two   con- 
densers together  in  parallel  the  positive  foils  of  one  are  joined 

to  the  positive  foils  of  the  other, 
and  their  negative  foils  are  also 
joined  together.  In  Fig.  176  the 
two  condensers  Ci  andC2  are  joined 
in  parallel.  They  will  thus  act 

FIG.  176. -Condensers  in  Parallel.    **&&  Uke   On6   lajge    ™ndenser  of 

capacity  =  Ci  +  C2.  Any  charge 

flowing  in  on  the  +  side  will  divide  between  the  two  in  pro- 
portion to  their  capacities. 

If  two  equal  Leyden  jars  are  charged  to  the  same  potential, 
and  then  their  inside  and  outside  coatings  are  respectively 
joined,  their  united  charge  will  be  the  same  as  that  of  a  jar 
of  equal  thickness,  but  having  twice  the  amount  of  surface. 

If  a  charged  Leyden  jar  is  placed  similarly  in  communica- 
tion with  an  uncharged  jar  of  equal  capacity,  the  charge 
will  be  shared  equally  between  the  two  jars,  and  the  pas- 


286  ELECTRICITY   AND  MAGNETISM      [PT.  n.  329 

sage  of  electricity  from  one  to  the  other  will  be  evidenced 
by  the  production  of  a  spark  when  the  respective  coatings 
are  put  into  communication.  Here,  however,  half  the  energy 
of  the  charge  is  lost  in  the  operation  of  sharing  the  charge, 
for  each  jar  will  have  only  J  Q  for  its  charge  and  J  V  for  its 
potential;  hence  the  energy  of  the  charge  of  each,  being 
half  the  product  of  charge  and  potential,  will  only  be  one 
quarter  of  the  original  energy.  The  spark  which  passes  in 
the  operation  of  dividing  the  charge  is,  indeed,  evidence  of 
the  loss  of  energy ;  it  is  about  half  as  powerful  as  the  spark 
would  have  been  if  the  first  jar  had  been  simply  discharged, 
and  it  is  just  twice  as  powerful  as  the  small  sparks  yielded 
finally  by  the  discharge  of  each  jar  after  the  charge  has  been 
shared  between  them. 

The  energy  of  a  charge  of  the  jar  manifests  itself,  as  stated 
above,  by  the  production  of  a  spark  at  discharge ;  the  sound, 
light,  and  heat  produced  being  the  equivalent  of  the  energy 
stored  up.  If  discharge  is  effected  slowly  through  a  long 
thin  wire  of  high  resistance  the  air  spark  may  be  feeble,  but 
the  wire  may  be  perceptibly  heated.  A  wet  string  being  a 
feeble  conductor  affords  a  slow  and  almost  silent  discharge  ; 
here  probably  the  electrolytic  conduction  of  the  moisture  is 
accompanied  by  an  action  resembling  that  of  secondary 
batteries  (Art.  572)  tending  to  prolong  the  duration  of  the 
discharge. 

329.  Capacities  joined  in  Series.  —  If  two  condensers  are 
joined  in  series  they  will  act  as  a  condenser  having  a  lesser  ca- 
pacity than  either  of  them  separately.  Their  joint  capacity 
in  series  will  be  the  reciprocal  of  the 
sum  of  the  reciprocals  of  their  capaci- 
ties separately. 


Proof.  —  Let  two  condensers  Ci  and 
C2  be  set  in  series  (Fig.  177)  between 
two  points  across  which  there  is  a  differ- 
ence of  potential  V.  This  difference  of  potential  will  be  divided 
between  the  two  inversely  in  proportion  to  their  capacities,  seeing 


CH.  iv.  329]  CAPACITIES   IN   SERIES  287 

that  the  quantities  of  electricity  that  are  displaced  into  and  out 
of  their  respective  coatings  are  necessarily  equal.  Or,  if  Q  be  this 
quantity,  and  C3  the  effective  or  joint  capacity  of  the  two  together, 
to  find  the  latter,  we  have  :  — 


Q  =  ViCi  =  V,C,  =  VC,        ...        (1) 

and  V  =  V!  +  V2         .      '.        .        .        .        (2) 

From  (1)  we  get 

Vi  =  VC,/Ci, 

and  V2  =  VC3/C2. 

Inserting  these  in  (2)  we  get 

V  =  VCs/d  +  VC3/C2; 
whence,  dividing  down  by  VC3,  we  get 


Example.'  —  If  two  condensers,  respectively  3  and  2  microfarads, 
are  joined  in  series,  they  will  act  as  a  single  condenser  of 
capacity  =  1/Q  +  i)  =  li  microfarads. 

Franklin  suggested  that  jars  might  be  arranged  in  series, 
the  outer  coating  of  one  being  connected  with  the  inner  one  of 
the  next,  the  outer  coating  of  the  last  being  connected  to 
earth.  The  object  of  this  arrangement  was  that  the  second 
jar  might  be  charged  with  the  electricity  repelled  from  the 
outer  coating  of  the  first,  the  third  from  that  of  the  second, 
and  so  on.  This  "  cascade  "  arrangement,  however,  is  of  no 
advantage,  the  sum  of  the  charges  accumulated  in  the  series 
being  only  equal  to  that  of  one  single  jar  if  used  alone.  For  if 
the  inner  coating  of  the  first  jar  be  raised  to  V,  that  of  the 
outer  coating  of  the  last  jar  remaining  at  zero  in  contact  with 
earth,  the  difference  of  potential  between  the  outer  and  inner 
coating  of  any  one  jar  will  be  only  V/w,  where  n  is  number  of 
jars.  And  as  the  charge  in  each  jar  is  equal  to  its  capacity 
C,  multiplied  by  its  potential,  the  charge  in  each  will  only 
be  CV/w,  and  in  the  whole  n  jars  the  total  charge  will  be 
n  X  CV/w,  or  CV,  or  equals  the  charge  of  one  jar  of  capacity 
C  raised  to  the  same  potential  V. 


288         ELECTRICITY  AND   MAGNETISM    [PT.  n.  330,  331 

LESSON  XXIV.  —  Phenomena  of  Discharge 

330.  Conductive    Discharge.  —  An    electrified    conductor 
may  be  discharged  in  at  least  three  different  ways,  depending 
on  the  medium  through  which  the  discharge  is  effected,  and 
varying  with  the  circumstances  of  the  discharge.     If  the 
discharge  takes  place  by  the  passage  of  a  continuous  current, 
as  when  electricity  flows  through  a  thin  wire  connecting  the 
knobs  of  an  influence  machine,  or  joining  the  positive  pole  of 
a  battery  to  the  negative  pole,  the   operation   is  termed  a 
"  conductive  "  discharge.     In  some  circumstances  a  conduc- 
tive discharge  takes  the  nature  of  an  oscillation  to  and  fro 
(Art.  600). 

331.  Disruptive  Discharge.  —  It  has  been  shown  how  in- 
fluence across  a  non-conducting  medium  is  always  accom- 
panied by  a  mechanical  stress  upon  the  medium ;  the  tension 
along  the  electric  lines  of  force  increasing  as  the  square  of 
the  intensity  of  the  electric  field.     If  this  stress  is  very  great 
the  non-conducting  medium  will  suddenly  break  down  and 
a  spark  will  burst  across  it.     Such  a  discharge  is  called  a 
"  disruptive  "  discharge, 

A  very  simple  experiment  will  set  the  matter  in  a  clear 
light.  Suppose  a  metal  ball  charged  with  +  electrification 
to  be  hung  by  a  silk  string  above  a  metal  plate  lying  on  the 
ground.  If  we  lower  down  the  suspended  ball  a  spark  will 
pass  between  it  and  the  plate  when  they  come  very  near  to- 
gether, and  the  ball  will  then  be  found  to  have  lost  all  its 
previous  charge.  It  was  charged  with  a  certain  quantity 
of  electricity ;  and  as  it  had,  when  suspended  out  of  the  range 
of  other  conductors,  a  certain  capacity  (numerically  equal  to 
its  radius  in  centimetres),  the  electricity  on  it  would  be  at  a 
certain  potential  (namely  =  Q/C),  and  the  charge  would  be 
distributed  uniformly  all  over  it.  The  plate  lying  on  the 
earth  would  be  all  the  while  at  zero  potential.  But  when  the 
suspended  ball  was  lowered  down  towards  the  plate  the  pre- 
vious state  of  things  was  altered.  In  the  presence  of  the  + 


CH.  iv.  332,  333]     CONVECTIVE    DISCHARGE  289 

charge  of  the  ball  the  potential 1  of  the  plate  would  rise,  were 
it  not  that,  by  influence,  just  enough  negative  electrification 
appears  on  it  to  keep  its  potential  still  the  same  as  that  of  the 
earth.  The  tension  in  the  electric  field  will  draw  the  + 
charge  of  the  ball  downwards,  and  alter  the  distribution  of 
the  charge,  the  surface-density  becoming  greater  at  the  under 
surface  of  the  ball  and  less  on  the  upper.  The  capacity 
of  the  ball  will  be  increased,  and  therefore  its  potential  will 
fall  correspondingly.  The  layer  of  air  between  the  ball  and 
the  plate  is  acting  like  the  glass  of  a  Ley  den  jar.  The  more 
the  ball  is  lowered  down  the  greater  is  the  accumulation  of 
the  opposite  kinds  of  charge  on  each  side  of  the  layer  of  air, 
and  the  tension  across  the  layer  becomes  greater  and  greater, 
until  the  limit  of  the  dielectric  strength  (Art.  335)  is  reached ; 
the  air  suddenly  gives  way  and  the  spark  tears  a  path  across. 

332.  Convective  Discharge.  —  A  third  kind  of  discharge, 
differing  from  either  of  those  above  mentioned,  may  take 
place,  and  occurs  chiefly  when  electricity  of  a  high  potential 
discharges  itself  at  a  pointed  conductor  by  accumulating  there 
with  so  great  a  density  as  to  electrify  the  neighbouring 
particles  of  air,  these  particles  then  flying  off  by  repulsion, 
conveying  away  part  of  the  charge  with  them.     Such  con- 
vective  discharges  may  occur  either  in  gases  or  in  liquids,  but 
are  best  manifested  in  air  and  other  gases  at  a  low  pressure, 
in  tubes  exhausted  by  an  air  pump. 

The  discharge  of  a  quantity  of  electricity  in  any  of  the 
above  ways  is  always  accompanied  by  a  transformation  of 
its  energy  into  energy  of  some  other  kind  —  sound,  light, 
heat,  chemical  actions,  and  other  phenomena  being  pro- 
duced. These  effects  must  be  treated  in  detail. 

333.  Length  of  Spark.  —  Generally  speaking,  the  length 
of  spark  between  two  conductors  increases  with  the  differ- 
ence between  their  potentials.     It  is  also  found  to  increase 

1  The  student  must  remember  that,   by  the  definition  of  potential  in 
Art.  280,  the  potential  at  a  point  is  the  sum  of  all  the  separate  quantities 
of  electricity  near  it,  divided  each  by  its  distance  from  the  point. 
U 


290  'ELECTRICITY   AND   MAGNETISM       [PT.  n.  333 

when  the  pressure  of  the  air  is  diminished.  Lord  Kelvin 
measured  by  means  of  an  "  absolute  electrometer  "  (Art. 
306)  the  difference  of  potential  necessary  to  produce  a  spark 
discharge  between  two  parallel  plates  at  different  distances. 
He  found  the  distance  to  increase  in  a  proportion  a  little 
exceeding  that  of  the  difference  of  potentials.  De  la  Rue  and 
Muller  found  with  their  great  battery  (Art.  197)  that  with  a 
difference  of  potential  of  1000  volts  the  striking  distance  of 
the  spark  was  only  0-0127  centimetre  (or  about  ^iu  of  an 
inch),  and  with  a  difference  of  10,000  volts  only  1-369  cms. 
Their  11,000  silver  cells  gave  a  spark  of  1-59  centim.  (about 
f  of  an  inch)  long.  To  produce  a  spark  one  mile  long,  through 
air  at  the  ordinary  pressure,  would  therefore  require  a  differ- 
ence of  potential  exceeding  that  furnished  by  1,000,000,000 
Daniell's  cells ! 

The  length  of  the  spark  differs  in  different  gases,  being 
nearly  twice  as  long  in  hydrogen  as  in  air  at  the  same  density. 
Or  to  produce  in  hydrogen  a  spark  as  long  as  one  in  air  re- 
quires less  voltage.  On  the  other  hand,  carbonic  acid  gas, 
whilst  it  is  stronger  than  air  for  short  sparks,  is  weaker  for 
long  ones. 

The  potential  needful  to  produce  a  spark  of  given  length 
in  a  given  gas  is  almost  independent  of  the  kind  of  metal 
used  as  electrodes,  but  depends  upon  their  shape.  If  points 
are  used  instead  of  balls  it  is  found  that,  at  equal  voltage, 
points  are  best  for  long  sparks,  but  are  worst  for  short  sparks. 

According  to  Strutt's  observations  a  minimum  potential 
of  341  volts  is  necessary  to  start  a  spark,  however  short,  in 
air.  For  sparks  not  under  two  millimeters  in  length  the  volts 
necessary  to  start  a  spark  across  a  length  of  I  centimetres 
may,  according  to  Peace,  be  approximately  expressed  by  the 
equation-  V  -  1600  +  30,000  L 

The  following  table,  calculated  from  the  results  of  Heyd- 
weiller,  gives  the  volts  necessary  to  produce  a  spark  in  air 
at  15°  C.  and  76  centimetres  pressure  between  two  spheres 


CH.  iv.  333] 


LENGTH   OF   SPARK 


291 


of  various  sizes.  The  figures  must  be  increased  1  per  cent 
for  a  fall  of  3  degrees  of  temperature,  or  for  a  rise  of  8  milli- 
metres of  pressure. 


DISTANCE  BETWEEN  BALLS  (Centims.) 

RADIUS  OF  BALLS 

O'l 

0-5 

ro 

1-5 

Centims. 

Volts. 

Volts. 

Volts. 

Volts. 

2'5 

4500 

18900 

33840 

47610 

ro 

4860 

18030 

32120 

41160 

0-5 

4950 

17790 

27810 

32400 

0-25 

4980 

16200 

20790 

22980 

For  long  sparks,  in  air,  the  potentials  to  produce  them 
are  practically  proportional  to  their  lengths. 

In  rarefied  air  the  spark  is  longer.  Snow  Harris  stated 
that  the  length  of  spark  was  inversely  proportional  to  the 
pressure,  but  this  law  is  not  quite  correct,  being  approxi- 
mately true  only  for  pressures  between  that  of  11  inches  of 
mercury  and  that  of  30  inches  (one  atmosphere).  At  lower 
pressures,  a  greater  difference  of  potential  must  be  used  to 
produce  a  spark  than  that  which  would  accord  with  Harris's 
law.  From  this  it  would  appear  that  thin  layers  of  air  op- 
pose a  proportionally  greater  resistance  to  the  piercing  power 
of  the  spark  than  thick  layers,  and  possess  greater  dielectric 
strength. 

Faraday,  using  two  spheres  of  different  sizes,  found  the 
spark-length  greater  when  the  smaller  sphere  was  positive 
than  when  it  was  negative. 

With  rapidly-alternating  differences  of  potential,  smaller 
virtual  voltages  suffice  for  the  same  spark-length,  for  the 
length  depend  son  the  maximum,  not  on  the  mean  value. 
Using  a  ball  of  1  cm.  diameter  and  a  disk,  Alexander  Siemens 
found  3200  virtual  volts  to  be  needed  at  0-1  cm.  distance, 
and  11,000  at  0-5  cm.  distance  apart. 

The  dielectric  strength  of  a  gas  appears  to  be  weaker  when 
field  is  varying  than  when  it  is  steady.  When  the  voltage 


292  ELECTRICITY   AND   MAGNETISM     [PT.  n.  334 

is  nearly  high  enough  to  produce  a  spark,  reversing  the  poles 
will  sometimes  start  a  spark.  Moreover,  when  once  a  spark 
has  passed  it  is  easier  for  a  second  one  to  follow  on  the  same 
track.  Probably  the  first  spark  produces  in  its  path  chemi- 
cal dissociations  which  do  not  instantly  pass  away. 

Hertz  made  the  singular  observation  that  ultra-violet 
light  (i.e.  actinic  waves)  falling  upon  the  kathode  surface 
assist  it  to  discharge  (see  Art.  619). 

A  perfect  vacuum  is  a  perfect  insulator  —  no  spark  will 
cross  it.  On  the  other  hand,  a  great  increase  of  pressure 
also  increases  the  dielectric  strength  of  air,  and  causes  it 
to  resist  the  passage  of  a  spark.  Cailletet  compressed  dry 
air  at  40  to  50  atmospheres'  pressure,  and  found  that  the 
spark  of  an  induction  coil  failed  to  cross  a  space  of  0-05 
centimetre's  width. 

334.  Flames  and  Hot  Air.  —  The  arc  produced  by  the 
passage  of  an  electric  current  between  two  carbon  pencils 
is  treated  of  in  Art.  486.  It  is  a  species  of  flame  which  con- 
ducts the  current  from  the  tip  of  one  carbon  rod  to  the  other, 
while  volatilizing  the  carbon,  and  requires  some  thirty  to 
fifty  volts  for  its  maintenance.  The  alternating-current 
arc  generated  in  air  by  high-frequency  discharges  at  a  poten- 
tial of  10,000  to  50,000  volts  is  a  different  phenomenon,  and 
is  apparently  an  endothermic  flame  of  nitrogen  and  oxygen 
burned  together. 

Sparks  are  longer  and  straighter  through  hot  air  than 
through  cold.  If  air  or  other  permanent  gas  is,  however, 
heated  in  a  closed  vessel  so  that  its  density  remains  unaltered, 
the  voltage  needful  to  produce  discharge  remains  the  same ; 
unless,  indeed,  the  gas  be  heated  to  point  of  dissociation, 
when  discharge  occurs  at  low  voltage. 

Flames  and  currents  of  very  hot  air,  such  as  those  rising 
from  a  red-hot  piece  of  iron,  are  extremely  good  conductors 
of  electricity,  and  act  even  better  than  metallic  points  in  dis- 
charging a  charged  conductor.  Gilbert  showed  that  an  elec- 
trified body  placed  near  a  flame  lost  its  charge ;  and  the  very 


CH.  iv.  335]  MECHANICAL   EFFECTS  293 

readiest  way  to  rid  the  surface  of  a  charged  body  of  low  con- 
ducting power  of  a  charge  imparted  to  it  by  friction  or  other- 
wise, is  to  pass  it  through,  or  hold  it  near  to,  the  flame  of  a 
spirit-lamp.  Faraday  found  negative  electrification  to  be 
thus  more  easily  discharged  than  positive.  Flames  power- 
fully negatively  electrified  are  repelled  from  conductors,  though 
not  so  when  positively  electrified.  Sir  W.  Grove  showed 
that  a  current  is  set  up  in  a  platinum  wire,  one  end  of  which 
touches  the  tip,  and  the  other  the  base,  of  a  flame. 

Guthrie  showed  that  a  red-hot  iron  ball  cannot  be  posi- 
tively, but  may  be  negatively  charged.  When  white-hot  it 
will  retain  neither  kind  of  charge. 

335.  Mechanical  Effects ;  Dielectric  Strength.  —  Chief 
amongst  the  mechanical  effects  of  the  disruptive  spark 
discharge  is  the  shattering  and  piercing  of  insulators.  The 
dielectric  strength  of  glass,  though  much  greater  than  that  of 
air,  is  not  infinitely  great.  A  slab  of  glass  3  inches  thick  has 
been  pierced  by  the  discharge  of  a  powerful  induction  coil. 
The  so  called  "  toughened  "  glass  has  a  greater  dielectric 
strength  than  ordinary  glass,  and  is  more  difficult  to  pierce. 
A  sheet  of  glass  may  be  readily  pierced  by  a  spark  from  a  large 
Ley  den  jar  or  battery  of  jars,  by  taking  the  following  pre- 
cautions :  —  The  sheet  to  be  pierced  is  laid  upon  a  block  of 
glass  or  resin,  through  which  a  wire  is  led  by  a  suitable  hole, 
one  end  of  the  wire  being  cut  off  flush  with  the  surface, 
and  the  other  end  being  connected  with  the  outer  coating  of 
the  jar.  Upon  the  upper  surface  of  the  sheet  of  glass  that  is 
to  be  pierced  another  wire  is  fixed  upright,  its  end  being  ex- 
actly opposite  the  lower  wire,  the  other  extremity  of  this 
wire  being  armed  with  a  metal  knob  to  receive  the  spark  from 
the  knob  of  the  jar  or  discharger.  To  ensure  good  insulation 
a  few  drops  of  paraffin  oil,  or  of  olive  oil,  are  placed  upon  the 
glass  round  the  points  where  the  wires  touch  it.  A  piece  of 
dry  wood  similarly  treated  is  split  by  a  powerful  spark.  A 
layer  of  oil  resists  being  pierced  as  much  as  a  layer  of  air  five 
or  six  times  as  thick  would  do. 


294  ELECTRICITY   AND   MAGNETISM     [PT.  n.  336 

The  dielectric  strength,  or  resistance  to  piercing  by  a  spark, 
is  most  conveniently  stated  in  terms  of  the  voltage  needed 
to  pierce  a  layer  one  millimetre  thick.  For  dry  paper  the 
limit  varies  from  1400  to  8000  volts;  for  varnished  paper, 
10,000  to  28,000 ;  gutta-percha,  7700  to  19,000 ;  india-rubber, 
16,000  to  21,000;  ebonite,  28,000  to  31,000;  mica,  from 
60,000  to  200,000 ;  dry  paraffin  oil,  30,000  to  100,000. 

If  a  spark  is  led  through  a  tightly-corked  glass  tube  con- 
taining water,  the  tube  will  be  shattered  into  small  pointed 
fragments  by  the  sudden  expansion  of  the  liquid. 

Lullin  observed  two  curious  effects  when  a  piece  of  card- 
board is  perforated  by  a  spark  between  two  metal  points. 
First,  there  is  a  slight  burr  raised  on  each  side,  as  if  the  hole 
had  been  pierced  from  the  middle  outwards,  as  though  the 
stress  in  the  air  had  pulled  at  the  card.  Secondly,  if  the  two 
points  are  not  exactly  opposite  one  another  the  hole  is  found 
to  be  nearer  the  negative  point.  But  if  the  experiment  is 
tried  under  the  air  pump  in  a  vacuum,  there  is  no  such  dis- 
placement of  the  hole ;  it  is  then  midway  exactly. 

The  mechanical  action  of  the  brush  discharge  at  points  is 
mentioned  in  Art.  47,  p.  50. 

336.  Chemical  Effects.  —  The  chemical  actions  produced 
by  currents  of  electricity  have  been  described  in  Lessons  XIV. 
and  XIX.  Similar  actions  can  be  produced  by  the  electric 
spark,  and  by  the  silent  glow  discharge  (see  Art.  340). 
Faraday  showed,  indeed,  that  electricity  from  all  kinds  of 
different  sources  produced  the  same  kinds  of  chemical  actions, 
and  he  relied  upon  this  as  one  proof  of  the  essential  identity 
of  the  electricity  produced  in  different  ways.  If  sparks  from 
an  electric  machine  are  received  upon  a  piece  of  white  blotting- 
paper  moistened  with  a  solution  of  iodide  of  potassium, 
brown  patches  are  noticed  where  the  spark  has  effected  a 
chemical  decomposition  and  liberated  the  iodine. 

When  a  stream  of  sparks  is  passed  through  moist  air  in 
a  vessel,  the  air  is  found  to  have  acquired  the  property  of 
changing  to  a  red  colour  a  piece  of  paper  stained  blue  with 


CH.  iv.  336]     CHEMICAL  ACTION   OF   SPARKS  295 

litmus.  This,  Cavendish  showed,  was  due  to  the  presence 
of  nitric  acid,  produced  by  the  chemical  union  of  the  nitrogen 
and  oxygen  of  the  air.  The  effect  is  best  shown  with  the 
stream  of  sparks  yielded  by  a  small  induction  coil  (Fig.  150), 
in  a  vessel  in  which  the  air  has  been  compressed  beyond  the 
usual  atmospheric  pressure. 

The  commercial  manufacture  of  nitric  acid  and  of  nitrates 
from  atmospheric  air  by  subjecting  it  to  powerful  electric 
discharges  in  a  special  electric  furnace  has  recently  been 
established  on  a  large  scale  in  Norway  by  Birkeland  and 
Eyde  (seep.  572). 

Whenever  an  electric  machine  is  giving  out  high-voltage 
discharges  a  peculiar  odour  is  perceived.  This  was  formerly 
thought  to  be  evidence  of  the  existence  of  an  electric  "  efflu- 
vium "  or  fluid ;  it  is  now  known  to  be  due  to  the  presence 
of  ozone,  a  modification  of  oxygen  gas,  which  differs  from 
oxygen  in  being  denser,  more  active  chemically,  and  in  having 
a  characteristic  smell.  The  silent  discharge  of  the  influence 
machine  and  that  of  the  induction  coil  are  particularly  fa- 
vourable to  the  production  of  this  substance.  The  spark 
and  brush  forms  of  discharge  produce  nitric  oxide,  not 
ozone. 

The  spark  will  decompose  ammonia  gas,  and  olefiant 
gas,  and  it  will  also  cause  chemical  combination  to  take 
place  with  explosion,  when  passed  through  detonating  mix- 
tures of  gases.  Thus  equal  volumes  of  chlorine  and  hydro- 
gen are  exploded  by  the  spark.  So  are  oxygen  and  hydro- 
gen gases,  when  mixed  in  the  proportion  of  two  volumes  of 
the  latter  to  one  of  the  former.  Even  the  explosive  mixture 
of  common  coal  gas  mixed  with  from  four  to  ten  times  its 
own  volume  of  common  air,  can  be  thus  detonated.  A 
common  experiment  with  the  so-called  electric  pistol  consists 
in  filling  a  small  brass  vessel  with  detonating  gases  and  then 
exploding  them  by  a  spark.  The  spark  discharge  is  some- 
times applied  to  the  firing  of  blasts  and  mines  in  military 
operations. 


296  ELECTRICITY   AND   MAGNETISM      [PT.  H.  337 

337.  Heating  Effects.  —  The  flow  of  electricity  through  a 
resisting  medium  is  in  every  case  accompanied  by  an  evolu- 
tion of  heat.  The  laws  of  heating  due  to  currents  are  given  in 
Art.  462.  The  disruptive  discharge  is  a  transfer  of  electricity 
through  a  medium  of  great  resistance  and  is  accompanied 
by  an  evolution  of  heat.  A  few  drops  of  ether  in  a  metallic 
spoon  are  easily  kindled  by  an  electric  spark.  The  spark 
from  an  electric  machine,  or  even  from  a  rubbed  glass  rod, 
suffices  to  kindle  an  ordinary  gas-jet.  In  certain  districts  of 
America,  during  the  driest  season  of  the  year,  the  mere  rub- 
bing of  a  person's  shoes  against  the  carpet,  as  he  shuffles 
across  the  floor,  generates  sufficient  electrification  to  enable 
sparks  to  be  drawn  from  his  body,  and  he  may  light  the  gas 
by  a  single  spark  from  his  outstretched  finger.  Gunpowder 
can  be  fired  by  the  discharge  of  a  Ley  den  jar,  but  the  spark 
should  be  retarded  by  being  passed  through  a  wet  thread, 
otherwise  the  powder  will  simply  be  scattered  by  the  spark. 

The  heating  powers  of  the  discharge  may  be  investi- 
gated by  causing  it  to  pass  through  a  glass  vessel  enclosing 
air,  and  communicating  with  a  tube  partly  filled  with  water 
or  other  liquid,  in  order  to  observe  changes  of  volume  or  of 
pressure.  Into  this  vessel  are  led  two  metal  rods,  between 
which  is  suspended  a  thin  wire,  or  a  filament  of  gilt  paper ; 
or  a  spark  can  be  allowed  simply  to  cross  between  them. 
When  the  discharge  passes  the  enclosed  air  is  heated,  expands, 
and  causes  a  movement  of  the  indicating  column  of  liquid. 
The  results  of  observation  with  these  instruments  are  as  fol- 
lows :  —  The  heating  effect  produced  by  a  given  charge  in  a 
wire  of  given  length  is  inversely  proportional  to  the  square  of 
the  area  of  the  cross  section  of  the  wire.  The  total  heat 
evolved  is  jointly  proportional  to  the  charge  and  to  the  po- 
tential through  which  it  falls.  In  fact,  if  the  entire  energy 
of  the  discharge  is  expended  in  producing  heat,  and  in  doing 
no  other  kind  of  work,  then  the  heat  developed  will  be  the 
thermal  equivalent  of  J  QV  ergs,  or  QV  -f-  2  J  calories ;  where 
J  represents  the  mechanical  equivalent  of  heat  (J  =  42 


CH.  iv.  338, 339]     HEATING  EFFECT   OF   SPARKS  297 

million;    since  42  X  10 6  ergs  =  1  calorie),  and  Q  and  V  are 
expressed  in  C.G.S.  units. 

When  a  powerful  discharge  takes  place  through  very  thin 
wires,  they  may  be  heated  to  redness,  and  even  fused  by 
the  heat  evolved.  A  narrow  strip  of  tinfoil  is  readily  fused 
by  the  charge  of  a  large  Ley  den  jar,  or  battery  of  jars.  A 
piece  of  gold  leaf  is  in  like  manner  volatilized  by  a  powerful 
discharge.  Franklin  utilized  this  property  for  a  rude  process 
of  multiplying  portraits  or  other  patterns,  which,  being  first 
cut  out  in  card,  were  reproduced  in  a  silhouette  of  metallic 
particles  on  a  second  card,  by  the  device  of  laying  above  them 
a  film  of  gold  or  silver  leaf  covered  again  with  a  piece  of  card 
or  paper;  a  Leyden  battery  being  then  discharged  through 
the  leaf. 

338.  Sparking  at  Contacts.  —  The  sparks  which  appear 
at  the  breaking  of  any  circuit  in  which  a  current  is  flowing 
(see  Art.  503)  cause  a  few  particles  of  the  metal  to  be  fused 
and  volatilized ;   and  if  repeated,  roughen  the  surface  where 
they  occur.     To  prevent  too  great  deterioration  of  the  con- 
tact surfaces,  keys  and  the  vibrating  contacts  of  electric 
bells  and  induction  coils  are  usually  provided  with  contact 
pieces  of  platinum  or  nickel,  or,  for  cheapness,  of  german 
silver.     Electric  light  switches  are  usually  provided  with 
copper  contact  surfaces,  and  are,  by  application  of  springs, 
made  to  snap  suddenly  apart,  on  break  of  circuit,  to  prevent 
the  spark  becoming  a  persistent  arc. 

339.  Luminous    Effects.  —  The    discharge    through    air 
exhibits  many  beautiful  and  varied  luminous  effects  under 
different  conditions.     The  spark  of  the  disruptive  discharge 
is  usually  a  thin  brilliant  streak  of  light.     When  it  takes  place 
between  two  metallic  balls,  separated  only  by  a  short  inter- 
val, it  usually  appears  as  a  single  thin  and  brilliant  line.     If, 
however,  the  distance  be  as  much  as  a  few  centimetres,  the 
spark  takes  an  irregular  zigzag  form.     In  any  case  its  path 
is  along  the  line  of  least  resistance,  the  presence  of  minute 
motes  of  dust  floating  in  the  air  being  quite  sufficient  to 


298  ELECTRICITY   AND   MAGNETISM      [PT.  n.  340 

determine  the  zigzag  character.  Often  the  spark  exhibits 
curious  ramifications  and  forkings,  of  which  an  illustration 
is  given  in  Fig.  178,  which  is  drawn  one-eighth  of  the  actual 
size  of  the  spark  obtained  from  an  electrical  machine.  They 
appear  to  be  drainage  lines  of  electrons  flowing  from  various 
points  and  uniting  in  streams  as  they  proceed  to  the  positive 
pole.  Photographs  of  lightning  flashes  almost  always  show 
similar  branching.  The  discharge  from  a  Ley  den  jar  affords 
a  much  brighter,  shorter,  noisier  spark  than  the  spark  drawn 
direct  from  the  collector  of  a  machine,  The  length  (see 
Art.  333)  depends  upon  the  potential,  and  upon  the  pressure 


FIG.  178.  —  Forked  Electric  Spark. 

and  temperature  of  the  air  in  which  the  discharge  takes  place. 
The  brilliance  depends  chiefly  upon  the  quantity  of  the  dis- 
charge. The  colour  of  the  spark  varies  with  the  nature  of 
the  metal  surfaces  between  which  the  discharge  takes  place ; 
for  the  spark  tears  away  in  its  passage  small  portions  of  the 
metal  surfaces,  and  volatilizes  them.  Between  copper  or 
silver  terminals  the  spark  takes  a  green  tint,  while  between 
iron  knobs  it  is  of  a  reddish  hue.  Examination  with  the  spec- 
troscope reveals  the  presence  in  the  spark  of  the  rays  charac- 
teristic of  the  incandescent  vapours  of  the  several  metals. 

340.  Brush  Discharge  :  Glow  Discharge.  —  If  an  electric 
machine  is  vigorously  worked,  but  no  sparks  be  drawn  from 
its  collector,  a  fine  diverging  brush  of  pale  blue  light  can  be 
seen  (in  a  dark  room)  streaming  from  the  brass  ball  at  the  end 
of  it  farthest  from  the  collecting  comb ;  a  hissing  or  crackling 
sound  always  accompanies  this  kind  of  discharge.  The  brush 


CH.  iv.  340]  LUMINOUS   DISCHARGES  299 

discharge  consists  of  innumerable  fine  twig-like  ramifications, 
presenting  a  form  of  which  Fig.  179  gives  a  fine  example; 
The  brightness  and  size  of  the  brush  is  increased  by  holding 
a  flat  plate  of  metal  a  little  way  from  it.  With  a  smaller  ball, 
or  with  a  bluntly-pointed  wire,  the  brush  appears  smaller, 
but  is  more  dis- 
tinct and  continu- 
ous. When  dis- 
charge is  going  on 
between  two  balls 
the  brushes  are 
never  alike.  At  the 
positive  ball  or 
anode  the  brush 
discharge  is  larger 
and  more  ramified 
than  at  the  nega- 
tive ball.  But  the  FlG" 179'  r  Electric  Bruah  (Positive) 
negative  brush  is  more  easily  formed  than  the  positive. 
Wheatstone  found  by  using  his  rotating  mirror  that  the 
brush  discharge  is  really  a  series  of  successive  partial  sparks 
at  rapid  intervals.  Metallic  dust  is  in  every  case  torn  away 
from  the  electrode  b}^  the  brush  discharge. 

If  the  blunt  or  rounded  conductor  be  replaced  by  a  pointed 
one,  the  brush  disappears  and  gives  place  to  a  silent  and  con- 
tinuous glow  where  the  electrified  particles  of  air  are  stream- 
ing away  at  the  point.  If  these  convection-streams  are  im- 
peded the  glow  may  once  more  give  place  to  the  brush. 
Where  a  negative  charge  is  being  discharged  at  a  point,  the 
glow  often  appears  to  be  separated  from  the  surface  of  the 
conductor  by  a  dark  space,  where  the  air,  without  becoming 
luminous,  still  conveys  the  electricity.  This  phenomenon, 
to  which  Faraday  gave  the  name  of  the  "  dark  "  discharge,  is 
very  well  seen  when  electricity  is  discharged  through  rarefied 
air  and  other  gases  in  vacuum  tubes. 

A  spark  discharge  may  degenerate  into  a  brush  if  the  sur- 


300         ELECTRICITY   AND   MAGNETISM     [PT.  n.  341,  342 

face  of  the  electrode  becomes  pitted  or  roughened  by  fre- 
quent discharges.  Hence  in  all  spark  experiments  it  is 
important  to  keep  the  discharging  balls  highly  polished. 

341.  The    Corona    Discharge.  —  When    alternating    cur- 
rents are  led  at  high  voltage  to  the  opposite  faces  of  a  thin 
glass  plate,  a  pale  violet  light  appears  at  the  edges  of  the 
electrodes,  when  the  alternating  pressure  is  raised  to  7000 
or  8000  volts.     On  raising  the  voltage  this  luminous  margin, 
which  is  called  the  corona,  becomes  broader  and  brighter; 
and  bright,  thin,  hot  streamers  dart  off  in  various  directions 
from  the  edges  of  the  electrodes.     At  20,000  volts  they  dart 
over  the  surface  of  the  plate  and  may  even  short-circuit  over 
the  edges  of  the  plate  with  noisy  coruscations.     On  trans- 
mission lines  at  extra  high  voltages  the  corona  sometimes 
occurs  around  the  wires.     It  is  due  to  the  air  becoming  con- 
ductive when  greatly  heated. 

342.  Discharges    in    Partial    Vacua.  —  If    the    discharge 
takes  place  in  glass  tubes  or  vessels  from  which  the  air  has 
been  partially  exhausted,  many  remarkable  and  beautiful 
luminous  phenomena  are  produced.     A   common  form  of 
vessel  is  the  "  electric  egg,"  a  sort  of  oval  bottle  that  can  be 
screwed  to  an  air  pump,  and  furnished  with  brass  knobs  to 
lead  in  the  sparks.     More  often  vacuum  tubes,  such  as  those 
manufactured   by   the   celebrated   Geissler,    are   employed. 
These  are  merely  tubes  of  thin  glass  blown  into  bulbous  or 
spiral  forms,  provided  with  two  electrodes  of  platinum  wire 
fused  into  the  glass,  and  sealed  off  after  being  partially  ex- 
hausted of  air  by  a  mercurial  air  pump.     Some  Geissler 
tubes  consist  of  two  bulbs  joined  by  a  narrow  tube  (Fig.  180), 
the  luminous  effects  being  usually  more  intense  in  the  con- 
tracted portion.     Such  tubes  are  readily  illuminated  by  dis- 
charges from  an  electrophorus  or  an  influence  machine ;  but 
it  is  more  common  to  work  them  with  the  spark  of  an  in- 
duction  coil    (Fig.    150).     A   coil   capable   of  producing   a 
J-inch  spark  in  air  will  illuminate  a  vacuum  tube  6  or  8 
inches  long.     Where  an  alternating  current  supply  is  avail- 


CH.  iv.  342]  DISCHARGES   IN   VACUA  301 

able,  small  transformers  (Art.  245)  wound  to  deliver  7V 
ampere  at  5000  volts  serve  admirably  for  lighting  vacuum 
tubes. 

Through  such  tubes,  before  exhaustion,  ordinary  sparks 
can  be  sent  only  by  using  enormous  electromotive  forces. 
As  the  air  is  exhausted  the  sparks  become  less  sharply 
defined,  and  widen  out  to  occupy  the  whole  tube,  becoming 
pale  in  tint  and  nebulous  in  form.  As  the  rarefied  air  offers 
much  less  resistance,  the  discharge  passes  freely.  The 
kathode  exhibits  a  beautiful  bluish  or  violet  glow,  separated 
from  the  conductor  by  a  narrow  dark  space,  while  at  the 
anode  a  single  small  bright  star  of  light  is  all  that  remains. 


FIG.  180.  —  Discharge  in  a  Vacuum  Tube. 

At  a  certain  degree  of  exhaustion  the  light  in  the  tube  breaks 
up  into  a  set  of  strice,  or  patches  of  light  of  a  cup-like  form, 
which  vibrate  to  and  fro  between  darker  spaces.  In  nitrogen 
gas  the  violet  aureole  glowing  around  the  kathode  is  very 
bright,  the  rest  of  the  light  being  rosy  in  tint.  In  oxygen 
the  difference  is  not  so  marked.  In  hydrogen  gas  the  tint 
of  the  discharge  is  bluish,  except  where  the  tube  is  narrow, 
where  a  beautiful  crimson  may  be  seen.  With  carbonic 
acid  gas  the  light  is  remarkably  white.  Particles  of  metal 
are  torn  off  from  the  kathode,  and  projected  from  its'  surface. 
The  kathode  is  usually  the  hotter  of  the  two  electrodes  when 
made  of  similar  dimensions  to  the  anode.  If  the  anode  is 
heated  and  the  kathode  kept  cool  no  discharge  will  pass.  If 
the  kathode  becomes  white-hot  the  glow  disappears,  and  the 


302  ELECTRICITY   AND   MAGNETISM     [PT.  n.  343 

gas  conducts  freely  without  shining.  The  luminosity  dis- 
appears from  the  rarefied  air  in  the  neighbourhood  of  a  red- 
hot  platinum  spiral  inside  the  tube.  It  is  also  observed 
that  the  light  of  these  discharges  in  vacuo  is  rich  in  those 
rays  which  produce  phosphorescence  and  fluorescence. 
Many  beautiful  effects  are  therefore  produced  by  blowing 
tubes  in  uranium  glass  (which  fluoresces  with  a  fine  green 
light),  or  by  placing  solutions  of  quinine  or  other  fluorescent 
liquids  in  outer  tubes  of  glass. 

343.  Phenomena  in  High  Vacua.  —  Sir  Wm.  Crookes 
found  that  when  exhaustion  is  carried  to  a  very  high  degree 
the  dark  space  separating  the  negative  glow  from  the  nega- 
tive pole  increases  in  width;  and  that  across  this  space 
electrified  particles  are  projected  in  straight  paths  in  direc- 
tions normal  to  the  surface  of  the  kathode,  and  independent 
of  the  position  of  the  anode.  If  exhaustion  be  carried  to 
such  a  high  degree  that  about  one-millionth  part  only  of  the 

air  remains,  the  dark  space  fills 
the  entire  tube  or  bulb,  the 
glass  walls  become  beautifully 
phosphorescent.  Diamonds, 
rubies,  and  even  white  pow- 
dered alumina  placed  in  the 
tubes  become  brilliantly  phos- 
phorescent if  the  kathode  dis- 
FIG.  isi.  —  Kathode  Discharge  in  charge  is  directed  upon  them. 

And     if     a     body     (whether 

opaque  or  transparent)  be  placed  in  front  of  the  electrode, 
a  sharply  defined  shadow  of  the  body  is  projected  upon  the 
opposite  wall  of  the  vessel,  showing  by  its  position  that  a 
stream  capable  of  producing  phosphorescence  proceeds  in 
straight  lines  from  the  kathode  and  is  intercepted  by  the 
body.  In  Fig.  181  the  kathode  K  is  a  slightly  convex  disk 
of  aluminium,  but  the  discharge  is  independent  of  the  metal 
used  as  kathode.  In  the  path  of  the  discharge  is  set  a  cross 
cut  out  of  mica.  Its  shadow  S  appears  on  the  end  of  the 


CH.  iv.  344]  KATHODE    RAYS  303 

bulb,  which  phosphoresces  all  around  the  shadowed  'part. 
The  anode  may  be  either  at  A  or  a.  Lightly-poised  vanes, 
if  placed  in  the  path  of  the  discharge,  are  driven  round  by 
the  mechanical  pressure  of  the  flying  particles. 

344.  Kathode  Rays  and  Canal  Rays.  —  These  kathodic 
discharges  are  deflected  from  their  straight  path  by  the 
action  of  a  magnetic  field,  and  were  found  by  Crookes  to  be 
deflected  as  though  they  were  negative  currents,  that  is  as 
though  they  conveyed  electricity  toward  the  kathode ;  sug- 
gesting that  they  were  negatively  charged.  Crookes  re- 
garded this  kathode  discharge  as  exhibiting  matter  in  an 
ultra-gaseous  or  radiant  state.  In  their  physical  properties 
the  kathode  "  rays "  closely  resemble  the  "  beta "  rays 
emitted  by  radium  (Art.  638).  Hertz  discovered  that  these 
kathode  "  rays  "  which  will  not  pass  through  glass,  mica,  or 
any  transparent  substance,  will  pass  through  metal  foil. 
Lenard,  using  a  vacuum 
tube  with  a  "  window  "  of 
aluminium  foil  at  one  end, 
succeeded  in  passing  the 

kathode    rays    OUt    into    the  FlG-  182>  ~~  Perrin's  Experiment  with 

.  J  Cylinder. 

air  (in  which  they  cannot 

be  produced  at  all),  and  found  them  to  retain  their  property 
of  exciting  phosphorescence.  Perrin  proved  that  the  kathode 
discharge  beam  carried  negative  charges,  by  directing  the 
discharge  from  the  kathode  K,  Fig.  182,  into  a  small  hollow 
cylinder  C,  surrounded  by  another  hollow  insulated  cylinder  A. 
The  cylinder  C  was  connected  to  an  electroscope  outside, 
which  became  negatively  charged.  But  if  by  means  of  a 
magnet  the  kathode  stream  was  deflected  so  that  it  did  not 
enter  C,  the  electroscope  remained  uncharged. 

In  a  series  of  brilliant  experiments  Sir  Joseph  J.  Thomson 
proved  the  correctness  of  Crookes's  hypothesis.  The  kathode 
"  rays  "  consist  of  streams  of  negatively  electrical  particles 
or  corpuscles  whose  mass  is  extraordinarily  small,  being  less 
than  T^Vfr  of  the  mass  of  a  hydrogen  atom.  The  speed  with 


304  ELECTRICITY  AND   MAGNETISM     [PT.  n.  345 

which  they  move  in  the  vacuum  tube  is  enormous,  being 
about  50,000  miles  per  second.  These  negative  corpuscles 
are  usually  called  electrons  (see  Lesson  LXIL,  Art.  630). 

If  the  kathode  is  perforated  with  a  hole  or  holes,  "  rays  " 
of  another  kind,  called  diakathodic  or  canal  rays,  are  ob- 
served  to   pass   in   pale   blue 
lines   through    the    apertures, 
Fig.  183.     These  rays,  which 
excite  a  different  kind  of  phos- 
183.  — Vacuum  Tube  showing      phorescence,  are  verv  slightly 

Canal  Rays. 

affected    by    a    magnet;    the 

deflexion  indicating  that  they  are  positively  charged.  Their 
speed  is  at  least  a  thousand  times  less  than  that  of  the  elec- 
trons, and  they  consist  probably  of  actual  atoms  of  gas 
positively  charged. 

345.  Striae  or  Stratifications.  —  The  striae,  mentioned 
in  Art.  342  above,  originate  at  the  anode  at  a  certain  pres- 
sure, and  become  more  numerous,  as  the  exhaustion  proceeds, 
up  to  a  certain  point,  when  they  become  thicker  and  diminish 
in  number,  until  exhaustion  is  carried  to  such  a  point  that 
no  discharge  will  pass.  Sir  Joseph  J.  Thomson  found  the 
column  of  striae  to  exhibit  a  nearly  constant  electric  resist- 
ance all  along;  though  beyond  it  in  the  neighbourhood  of 
the  kathode  the  resistance  was  much  greater.  In  a  vacuum 
tube  over  50  feet  long  the  discharge  was  striated  through  the 
whole  length  except  near  the  kathode.  If  the  kathode  is 
moved  forward  the  striae  move  with  it.  The  striae  flicker 
even  when  the  continuous  current  from  a  battery  of  some 
thousand  of  cells  (Art.  197)  is  used.  There  is  a  maximum 
of  steadiness  with  a  particular  density  of  current.  The 
striae  are  hotter  than  the  spaces  between  them.  The  num- 
ber and  position  of  the  striae  vary,  not  only  with  the  ex- 
haustion, but  with  the  difference  of  potentials  of  the  elec- 
trodes. Each  portion  of  the  column  of  striae  acts  as  an 
independent  discharge.  When  striae  are  produced  by  the 
intermittent  discharges  of  the  induction  coil,  examination 


CH.  iv.  346,  347]     VELOCITY   OF   PROPAGATION  305 

of  them  in  a  rotating  mirror  reveals  that  they  move  forward 
from  the  anode  towards  the  kathode. 

346.  lonization  by  Discharge.  —  Schuster  has  shown  that 
the  discharge  through  gases  is  a  process  resembling  that  of 
electrolysis  (Art.  253),  being  accompanied  by  breaking  up 
of  the  gaseous  molecules  and  incessant  interchanges  of  atoms 
between  them.     The  production  of  ozone  (Art.  336)  and  the 
phenomena  noticed  at  the  kathode  (Art.  343)  give  support 
to  this  view.     Amongst  other  evidence  is  the  striking  dis- 
covery of  Hittorf  that  quite  a  few  cells  can  send  a  current 
through  gas  at  ordinary  pressures  provided  a  spark-discharge 
is  going  on  in  the  neighbourhood.     Sir  Joseph  J.  Thomson 
finds  that  those  gases  which  when  heated  are  decomposed 
or  molecularly  dissociated,  so  that  free  atoms  are  present, 
are  then  good  conductors.     lonization  of  the  gas  appears 
to  be  an  essential  feature  of  gaseous  discharge. 

The  discharges  in  vacuum  tubes,  at  all  degrees  of  exhaus- 
tion, are  affected  by  the  magnet,  behaving  like  flexible  con- 
ductors. Under  certain  conditions  also,  the  discharge  is 
sensitive  to  the  presence  of  a  conductor  on  the  exterior  of 
the  tube,  retreating  from  the  side  where  it  is  touched. 

347.  Velocity  of  Propagation  of  Discharge.  —  The  earliest 
use  of  the  rotating  mirror  to  analyze  phenomena  of  short 
duration  was  made  by  Wheatstone,  who  attempted  by  this 
means  to  measure  "  the  velocity  of  electricity  "  in  conduct- 
ing wires.     What  he  succeeded  in  measuring  was  not,  how- 
ever, the  velocity  of  electricity,  but  the  time  taken  by  a  certain 
quantity  of  electricity  to  flow  through  a  conductor  of  con- 
siderable resistance   and   capacity.     Viewed   in   a  rotating 
mirror,   a  spark  of  definite  duration  would  appear  to  be 
drawn  out  into  an  elongated  streak.     Such  an  elongation 
was  found  to  be  visible  when  a  Ley  den  jar  was  discharged 
through  a  copper  wire  half  a  mile  long ;  and  when  the  circuit 
was  interrupted  at  three  points,  one  in  the  middle  and  one 
at  each  end  of  this  wire,  three  sparks  were  obtained,  which, 
viewed  in  the  mirror,  showed  a  lateral  displacement,  indi- 

x 


306  ELECTRICITY  AND   MAGNETISM     [PT.  n.  348 

eating  (with  the  particular  rate  of  rotation  employed)  that 
the  middle  spark  took  place  TTTTTTO  o"  °f  a  second  later  than 
those  at  the  ends.  Wheatstone  argued  from  this  a  velocity 
of  288,000  miles  per  second.  But  Faraday  showed  that  the 
apparent  rate  of  propagation  of  a  quantity  of  electricity 
must  be  affected  by  the  capacity  of  the  conductor;  and  he 
even  predicted  that  since  a  submerged  insulated  cable  acts 
like  a  Leyden  jar  (see  Art.  321),  and  has  to  be  charged  before 
the  potential  at  the  distant  end  can  rise,  it  will  retard  the 
apparent  flow  of  electricity  through  it.  There  is  in  fact  no 
definite  assignable  "  velocity  of  electricity."  In  the  case  of 
wires  suspended  in  air  the  velocity  of  propagation  of  any 
sudden  electrical  disturbance  is  equal  to  the  velocity  of  light. 
But  in  the  case  of  slow  vibrations,  like  those  of  telephonic 
sounds,  being  sent  through  land  lines  or  cables,  the  velocity 
may  be  much  less. 

A  very  simple  experiment  will  enable  the  student  to 
realize  the  exceedingly  short  duration  of  the  spark  of  a  Ley- 
den  jar.  Let  a  round  disk  of  cardboard  painted  with  black 
and  white  sectors  be  rotated  very  rapidly  so  as  to  look  by 
ordinary  light  like  a  mere  grey  surface.  When  this  is  illu- 
minated by  the  spark  of  a  Leyden  jar  it  appears  to  be  stand- 
ing absolutely  still,  however  rapidly  it  may  be  turning.  A 
flash  of  lightning  is  equally  instantaneous ;  it  is  utterly  im- 
possible to  determine  at  which  end  the  flash  begins.1 

348.  Electric  Dust-Figures.  —  Electricity  may  creep 
slowly  over  the  surface  of  bad  conductors.  Lichtenberg 
devised  an  ingenious  and  easy  way  of  investigating  the  dis- 
tribution of  electricity  by  means  of  certain  electroscopic 
powders.  Take  a  charged  Leyden  jar  and  write  with  the 
knob  of  it  upon  a  cake  of  pitch  or  a  dry  sheet  of  glass.  Then 
sift,  through  a  bit  of  muslin,  over  the  cake  a  mixture  of 

1  Sometimes  the  flash  seems  to  strike  downwards  from  the  clouds,  some- 
times upwards  from  the  earth.  This  is  an  optical  illusion,  resulting  from 
the  unequal  sensitiveness  to  light  of  different  portions  of  the  retina  of  the 
eye. 


CH.  iv.  348]  ELECTRIC    DUST-FIGURES  307 

powdered  red  lead  and  sulphur  (vermilion  and  lycopodium 
powder  answer  equally  well).  The  powders  in  this  process 
rub  against  one  another,  the  red  lead  becoming  +  ,  the  sul- 
phur — .  Hence  the  sulphur  will  be  attracted  to  those  parts 
where  theo*e  is  -f  electrification  on  the  disk,  and  settles  down 
in  curious  branching  yellow  streaks  like  those  shown  in  Fig. 
184.  The  red  lead  settles  down  in  little  red  heaps  and 
patches  where  the  electrification  is  negative.  These  rounded 
red  patches  indicate  that  the  —  discharge  has  been  of  the 


FIG.  184.  —  Lichtenberg's  Figure  (Positive). 

nature  of  a  wind  or  silent  discharge.  The  branching  yellow 
streaks  indicate  that  the  positive  discharge  (as  indeed  may 
be  heard)  is  of  the  nature  of  a  brush.  They  are  regarded  by 
Nipher  as  drainage  lines  where  the  electrons  pass  through 
the  dielectric  (air)  at  the  surface  of  the  sheet  of  pitch,  or 
glass.  Fig.  185  shows  the  general  appearance  of  the  Lichten- 
berg's  figure  produced  by  holding  the  knob  of  the  Leyden 
jar  at  the  centre  of  a  shellac  plate  that  has  previously  been 
rubbed  with  flannel,  the  negative  electrification  being  at- 
tracted upon  all  sides  toward  the  central  positive  charge. 
These  same  powders  may  be  used  to  investigate  how  sur- 


308  ELECTRICITY  AND   MAGNETISM     [PT.  n.  348 

faces  have  become  electrified  by  rubbing,  and  how  pyro- 
electric  crystals  (Art.  75)  are  electrified  during  cooling. 

Powdered  tourmaline,  warmed  and  then  sifted  over  a 
sheet  of  glass  previously  electrified  irregularly,  will  show 
similar  figures,  though  not  so  well  defined. 

Similar  figures  can  be  made  by  directing  a  spark  at  the 
surface  of  stiff  oil,  where  they  persist  for  a  short  time  and 
can  be  seen  without  using  powders.  If  a  spark  is  directed 
(in  the  dark)  on  a  photographic  dry  plate  that  is  then  de- 


FIG.  185.  —  Lichtenberg's  Figure  (Negative). 

veloped,  the  forms  are  permanently  preserved.  In  all  cases 
the  positive  discharge  always  produces  the  characteristic 
ramified  lines  like  those  of  Fig.  184. 

Breath-figures  can  be  made  by  electrifying  a  coin  or  other 
piece  of  metal  laid  upon  a  sheet  of  dry  glass,  and  then  breath- 
ing upon  the  glass  where  the  coin  lay,  revealing  a  faint 
image  of  it  on  the  surface  of  the  glass. 

Jervis-Smith  found  that  if  a  coin  or  engraving  laid  face- 
down upon  a  photographic  dry-plate  is  sparked  with  an 
induction  coil,  the  plate  receives  an  invisible  image  of  the 
object,  which  can  be  photographically  developed. 


CH.  iv.  349,  350]  LAW   OF   LEAKAGE  309 

349.  Physiological    Effects.  —  The    physiological    effects 
of  the  current  have  been  described  in  Lesson  XX.     Those 
produced  by  the  spark-discharge  are  more  sudden  in  char- 
acter, but  of  the  same  general  nature.     Death  is  seldom  the 
direct  result.     The  shock  causes  a  sudden  cessation  of  respira- 
tion, resulting  in  suffocation  as  from  drowning.     The  bodies 
of  persons  struck  by  the  lightning  spark  frequently  exhibit 
markings  of  a  reddish  tint  where  the  discharge  in  passing 
through  the  tissues  has  lacerated  or  destroyed  them.     Some- 
times these  markings  present  a  singular  ramified  appear- 
ance, like  those  of  Fig.  184. 

350.  Dissipation  of  Charge.  —  However  well  insulated  a 
charged  conductor  may  be,  and  however  dry  the  surrounding 
air,  it  nevertheless  slowly  loses  its  charge,  and  in  a  few  days 
will  be  found  to  be  completely  discharged.     The  rate  of  loss 
of  charge  is,   however,  not  uniform.     It  is  approximately 
proportional  to  the  difference  of  potential  between  the  body 
and  the  earth.     Hence  the  rate  of  loss  is  greater  at  first 
than  afterwards,  and  is  greater  for  highly-charged  bodies 
than  for  those  feebly  charged.     The  law  of  dissipation  of 
charge  therefore  resembles  Newton's  law  of  cooling,  accord- 
ing to  which  the  rate  of  cooling  of  a  hot  body  is  proportional 
to  the  difference  of  temperature  between  it  and  the  sur- 
rounding objects.     If  the  potential  of  the  body  be  measured 
at  equal  intervals  of  time  it  will  be  found  to  have  diminished 
in  a  decreasing  geometric  series;    or  the  logarithms  of  the 
potentials  at  equal  intervals  of  time  will  differ  by  equal 
amounts.     The  rate  of  loss  is,  however,  greater  at  negatively- 
electrified  surfaces  than  at  positive. 

This  may  be  represented  by  the  following  equation : 

V,  -  V0  e-6', 

where  V0  represents  the  original  potential  and  V*  the  potential 
after  an  interval  t.  Here  e  stands  for  the  number  2*71828  .  .  . 
(the  base  of  the  natural  logarithms),  and  b  stands  for  the  "  co- 
efficient of  leakage,"  which  depends  upon  the  temperature,  pres- 


310  ELECTRICITY   AND   MAGNETISM    [PT.  n.  351,  352 

sure,  and  humidity  of  the  air.  The  same  formula  serves  for  the 
discharge  of  a  condenser  of  capacity  C  through  a  resistance  R,  if  b 
is  written  for  1/CR. 

351.  Positive  and  Negative  Electrification.  —  The  stu- 
dent will  not  have  failed  to  notice  throughout  this  lesson 
frequent  differences  between  the  behaviour  of  positive  and 
negative  electrification.  The  striking  dissimilarity  in  the 
Lichtenberg's  figures,  the  displacement  of  the  perforation- 
point  in  Lullin's  experiment,  the  unequal  tendency  to  dissi- 
pation at  surfaces,  the  unequal  action  of  heat  on  positive 
and  negative  charges,  the  remarkable  differences  in  the 
various  forms  of  brush  and  glow  discharge,  are  all  points 
that  claim  attention.  Gassiot  described  the  appearance  in 
vacuum  tubes  as  of  a  force  emanating  from  the  negative  pole. 
Crookes's  experiments  in  high  vacua  (Art.  343),  show  cor- 
puscles to  be  violently  discharged  from  the  kathode;  the 
vanes  of  a  little  fly  enclosed  in  such  tubes  being  moved  from 
the  side  struck  by  the  kathodic  discharge.  Holtz  found  that 
when  funnel-like  partitions  were  fixed  in  a  vacuum  tube  the 
resistance  is  much  less  when  the  open  mouths  of  the  funnels 
face  the  kathode;  thus  constituting  a  species  of  valve  (see 

Art.  634).      These  mat- 
ters are  now  accounted 
for  by  the  electron  theory 
of  electricity  (Art.  630). 
352.   Roentgen's  Rays. 
-  In  1895  Roentgen  dis- 
covered that  highly  ex- 
hausted  tubes,   such    as 

FIG.  186.  —  Roentgen-ray  Tube.  ,  f  . 

the  Crookes  tubes  (Art. 

343),  when  stimulated  by  electric  discharges,  emit  some  in- 
visible rays,  which  he  called  X-rays,  having  very  remarkable 
properties.  They  excite  brilliant  fluorescence  on  such  sub- 
stances as  the  platinocyanide  of  barium ;  they  differ  from 
ultra-violet  light  and  other  invisible  kinds  of  radiation  in 
being  incapable  of  refraction,  or  of  regular  reflexion.  They 


CH.  iv.  353]  THUNDERSTORMS  311 

pass  freely  through  aluminium,  zinc,  wood,  paper,  and 
flesh,  but  not  through  lead,  platinum,  glass,  or  bone. 
They  also  act  on  ordinary  photographic  plates.  Hence 
it  is  possible  by  using  a  fluorescent  screen  to  see,  and 
by  using  sensitive  plates  to  photograph,  the  shadows  of 
such  things  as  the  bones  in  the  living  body,  or  the  bullet  in 
the  barrel  of  a  gun.  It  is  found  that  these  rays  are  given 
off,  inside  the  Crookes  tubes,  from  the  solid  surface  —  the 
glass  or  a  metal  target,  placed  inside  on  purpose  — against 
which  the  kathode  rays  are  directed.  Those  substances 
which  have  highest  atomic  weights  absorb  the  Roentgen 
rays  best,  or  if  used  as  targets  emit  them  best.  Hence  the 
target,  or  antikathode,  should  be  of  platinum,  uranium, 
osmium,  or  tungsten.  Fig.  186  depicts  a  Roentgen-ray  tube 
in  which  A  is  the  anode,  K  the  kathode,  shaped  as  a  shallow 
cup,  and  T  the  target  or  antikathode.  If  the  skin  be  exposed 
for  only  a  few  minutes  to  Roentgen  rays,  an  irritating  and 
even  dangerous  inflammation  may  result.  These  rays 
closely  resemble  in  their  properties  the  penetrative  " gamma" 
rays  emitted  from  radium.  (See  Art.  638,  p.  643.) 

LESSON  XXV.  —  Atmospheric  Electricity 

353.    The   Thunderstorm   an   Electrical   Phenomenon.  — 

The  phenomena  of  atmospheric  electricity  are  of  three  kinds. 
There  are  the  well-known  electrical  phenomena  of  thunder- 
storms; and  there  are  the  phenomena  of  continual  slight 
electrification  in  the  air,  best  observed  when  the  weather  is 
fine.  The  phenomena  of  the  polar  Aurora  constitute  a  third 
branch  of  the  subject. 

The  detonating  sparks  drawn  from  electrical  machines 
and  from  Leyden  jars  did  not  fail  to  suggest  to  the  early 
experimenters,  Hauksbee,  Newton,  Wall,  Nollet,  and  Gray, 
that  the  lightning  flash  and  the  thunderclap  were  due  to 
electric  discharges.  In  1749,  Benjamin  Franklin,  observing 
lightning  to  possess  almost  all  the  properties  observable  in 


312  ELECTRICITY   AND   MAGNETISM      [PT.  n.  354 

electric  sparks,1  suggested  that  the  electric  action  of  points 
(Art.  47),  which  was  discovered  by  him,  might  be  tried  on 
thunderclouds,  and  so  draw  from  them  a  charge  of  electricity. 
He  proposed,  therefore,  to  fix  a  pointed  iron  rod  to  a  high 
tower.  Before  Franklin  could  carry  his  proposal  into  effect, 
Dalibard,  at  Marly-la-ville,  near  Paris,  taking  up  the  hint, 
erected  an  iron  rod  40  feet  high,  by  which,  in  1752,  he  drew 
sparks  from  a  passing  cloud.  Franklin  shortly  after  suc- 
ceeded in  another  way.  He  sent  up  a  kite  during  the  pass- 
ing of  a  storm,  and  found  the  wetted  string  to  conduct  elec- 
tricity, to  the  earth,  and  to  yield  abundance  of  sparks. 
These  he  drew  from  a  key  tied  to  the  string,  a  silk  ribbon 
being  interposed  between  his  hand  and  the  key  for  safety. 
Ley  den  jars  could  be  charged,  and  many  other  electrical 
effects  produced,  by  the  sparks  furnished  from  the  clouds. 
The  proof  of  the  identity  was  complete.  The  kite  experi- 
ment was  repeated  by  Romas,  who  drew  from  a  metallic 
string  sparks  9  feet  long,  and  by  Cavallo,  who  made  many 
important  observations  on  atmospheric  electricity. 

354.  Theory  of  Thunderstorms.  —  Solids  and  liquids  can- 
not be  charged  throughout  their  substance ;  if  charged  at  all, 
the  electrification  is  upon  their  surface  (see  Art.  32).  But 
gases  and  vapours,  being  composed  of  myriads  of  separate 
particles,  can  receive  a  bodily  charge.  The  air  in  a  room 
in  which  an  electric  machine  is  worked  is  found  afterwards 
to  be  charged.  The  clouds  are  usually  charged  moio  or  less 
with  electricity,  derived,  probably,  from  evaporation  going 

1  Franklin  enumerates  specifically  an  agreement  between  electricity  and 
lightning  in  the  following  respects :  —  Giving  light ;  colour  of  the  light ; 
crooked  direction ;  swift  motion ;  being  conducted  by  metals ;  noise  in 
exploding  ;  conductivity  in  water  and  ice  ;  rending  imperfect  conductors  ; 
destroying  animals  ;  melting  metals  ;  firing  inflammable  substances ;  sul- 
phureous smell  (due  to  ozone,  as  we  now  know)  ;  and  he  had  previously 
found  that  needles  could  be  magnetized  both  by  lightning  and  by  the  elec- 
tric spark.  He  also  drew  attention  to  the  similarity  between  the  pale 
blue  flame  seen  during  thundery  weather  playing  at  the  tips  of  the  masts 
of  ships  (called  by  sailors  St.  Elmo's  Fire),  and  the  "glow"  discharge  at 
points. 


CH.  iv.  355]  LIGHTNING   FLASHES  313 

on  at  the  earth's  surface.  The  minute  particles  of  water 
floating  in  the  air  become  more  highly  charged.  As  they 
fall  by  gravitation  and  unite  together,  the  strength  of  their 
charges  increases.  Suppose  eight  small  drops  to  join  into 
one.  That  one  will  have  eight  times  the  quantity  of  elec- 
tricity distributed  over  the  surface  of  a  single  sphere  of 
twice  the  radius  (and,  therefore,  of  twice  the  capacity,  by 
Art.  291)  of  one  of  the  original  drops;  and  its  electrical 
potential  will  therefore  be  four  times  as  great.  Now  a 
mass  of  cloud  may  consist  of  such  charged  spheroids,  and  its 
potential  may  gradually  rise,  therefore,  by  the  coalescence 
of  the  drops,  and  the  electrification  at  the  lower  surface  of 
the  cloud  will  become  greater  and  greater,  the  surface  of  the 
earth  beneath  acting  as  a  condensing  plate  and  becoming 
charged,  by  influence,  with  the  opposite  kind  of  electrifica- 
tion. Presently  the  difference  of  potential  becomes  so  great 
that  the  intervening  strata  of  air  give  way  under  the  strain, 
and  a  disruptive  discharge  takes  place  at  the  point  where 
the  air  offers  least  resistance.  This  lightning  spark,  which 
may  be  more  than  a  mile  in  length,  discharges  only  the  elec- 
tricity that  has  been  accumulating  at  the  surface  of  the 
cloud,  and  the  other  parts  of  the  cloud  will  now  react  upon 
the  discharged  portion,  producing  internal  attractions  and 
internal  discharges.  The  internal  actions  thus  set  up  will 
account  for  the  usual  appearance  of  a  thundercloud,  that 
it  is  a  well-defined  flat-bottomed  mass  of  cloud  which  appears 
at  the  top  to  be  boiling  or  heaving  up  with  continual  move- 
ments. 

355.  Lightning  and  Thunder.  —  Three  kinds  of  lightning 
have  been  distinguished  by  Arago :  (i.)  The  Zigzag  flash  or 
"  Forked  lightning,"  of  ordinary  occurrence.  The  zigzag 
form  is  probably  due  either  to  the  presence  of  solid  particles 
in  the  air  or  to  local  electrification  at  certain  points,  making 
the  crooked  path  the  one  of  least  resistance,  (ii.)  Sheet 
lightning,  in  which  whole  surfaces  are  lit  up  at  once,  is  prob- 
ably only  the  reflexion  on  the  clouds  of  a  flash  taking  place 


314  ELECTRICITY   AND   MAGNETISM      JPT.  n.  355 

at  some  other  part  of  the  sky.  It  is  often  seen  on  the  hori- 
zon at  night,  reflected  from  a  storm  too  far  away  to  pro- 
duce audible  thunder,  and  is  then  known  as  "  summer  light- 
ning." (iii.)  Globular  lightning,  in  the  form  of  balls  of  fire, 
which  move  slowly  along  and  then  burst  with  a  sudden 
explosion.  This  form  is  very  rare,  but  must  be  admitted 
as  a  real  phenomenon,  though  some  of  the  accounts  of  it 
are  greatly  exaggerated.  Similar  phenomena  on  a  small 
scale  have  been  produced  (though  usually  accidentally)  with 
electrical  apparatus. 

The  sound  of  the  thunder  may  vary  with  the  conditions 
of  the  lightning  spark.  The  spark  heats  the  air  in  its  path, 
causing  sudden  expansion  and  compression  all  round,  fol- 
lowed by  as  sudden  a  rush  of  air  into  the  partial  vacuum  thus 
produced.  If  the  spark  be  straight  and  short,  the  observer 
will  hear  but  one  short  sharp  clap.  If  its  path  be  a  long  one 
and  not  straight,  he  will  hear  the  successive  sounds  one 
after  the  other,  with  a  characteristic  rattle,  and  the  echoes 
from  other  clouds  will  come  rolling  in  long  afterwards.  The 
lightning-flash  itself  never  lasts  more  than  iinnnnr  °f  a 
second,  but  sometimes  is  oscillatory  in  character  (see  Art. 
600). 

The  damage  done  by  a  lightning-flash  when  it  strikes  an 
imperfect  conductor  appears  sometimes  as  a  disruptive 
mechanical  disintegration,  as  when  the  masonry  of  a  chimney- 
stack  or  church-spire  is  overthrown,  and  sometimes  as  an 
effect  of  heat,  as  when  bell- wires  and  objects  of  metal  in  the 
path  of  the  lightning-current  are  fused.  The  physiological 
effects  of  sudden  discharges  are  discussed  in  Arts.  270  and  349. 

The  "  return-stroke "  experienced  by  persons  in  the 
neighbourhood  of  a  flash  is  explained  in  Art.  29. 

Often  two  or  more  successive  lightning  flashes  may  follow 
one  another  down  the  same  path.  The  probability  is  that 
the  first  flash  ionizes  (Art.  346)  the  air  in  its  neighbourhood, 
thus  providing  a  better  conducting  track  along  which  a 
second  flash  follows. 


CH.  iv.  356]          LIGHTNING   CONDUCTORS  315 

356.  Lightning  Conductors.  —  The  first  suggestion  to 
protect  property  from  destruction  by  lightning  was  made 
by  Franklin  in  1749,  in  the  following  words :  - 

"  May  not  the  knowledge  of  this  power  of  points  be  of  use  to 
mankind,  in  preserving  houses,  churches,  ships,  etc.,  from  the 
stroke  of  lightning,  by  directing  us  to  fix  on  the  highest  parts  of 
those  edifices  upright  rods  of  iron  made  sharp  as  a  needle,  and  gilt 
to  prevent  rusting,  and  from  the  foot  of  those  rods  a  wire  down 
the  outside  of  the  building  into  the  ground,  or  round  one  of  the 
shrouds  of  a  ship,  and  down  her  side  till  it  reaches  the  water? 
Would  not  these  pointed  rods  probably  draw  the  electrical  fire 
silently  out  of  a  cloud  before  it  came  nigh  enough  to  strike,  and 
thereby  secure  us  from  that  most  sudden  and  terrible  mischief?  " 

Maxwell  proposed  to  cover  houses  with  a  network  of  con- 
ducting wires,  without  any  main  conductor,  the  idea  being 
that  then  the  interior  of  the  building  will,  like  Faraday's 
hollow  cube  (Art.  34),  be  completely  protected  from  electric 
force.  Much  controversy  has  arisen  respecting  lightning- 
rods.  Sir  Oliver  Lodge  maintains  the  lightning  flash  to  be 
of  the  nature  of  an  electric  oscillation  (Art.  600)  rather  than 
a  current.  If  so,  the  conductor  of  least  resistance  is  not 
necessarily  the  best  lightning-rod.  Sir  Oliver  Lodge  and 
the  author  independently,  and  for  different  reasons,  recom- 
mend iron  in  preference  to  copper  for  lightning-rods. 

The  following  points  summarize  the  modern  views  on  the 
subject :  — 

1.  All  parts  of  a  lightning  conductor  should  be  of  one  and  the 
same  metal,  avoiding  joints  as  far  as  possible,  and  with  as  few 
sharp  bends  or  corners  as  may  be. 

2.  The  use  of  copper  for  lightning-rods  is  a  needless  extrava- 
gance.    Iron  is  far  better.     Ribbon  is  slightly  better  than  round 
rod ;  but  ordinary  galvanized  iron  telegraph-wire  is  good  enough. 

3.  The  conductor  should  terminate  not  merely  at  the  highest 
point  of  a  building,  but  be  carried  to  all  high  points.     It  is  unwise 
to  erect  very  tall  pointed  rods  projecting  several  feet  above  the 
roof. 

4.  A  good  deep  wet  "  earth  "  should  be  provided,  independent 
of  gas  or  water  pipes,  to  which  the  conductor  should  be  led  down. 


316  ELECTRICITY   AND   MAGNETISM      [PT.  n.  357 

5.  If  in  any  part  the  conductor  goes  near  a  gas  or  water  pipe 
it  is  better  to  connect  them  metallically  than  to  leave  them  apart. 

6.  In   ordinary   buildings    the   conductor   should   be    insulated 
away  from  the  walls,  so  as  to  lessen  liability  of  lateral  discharge  to 
metal  stoves  and  things  inside  the  house. 

7.  Connect    all    external    metal-work,    zinc    spouts,    iron    crest 
ornaments,  and  the  like,  to  each  other,  and  to  the  earth,  but  not  to 
the  lightning  conductor. 

8.  The  cheapest  way  of  protecting  an  ordinary  house  is  to  run 
common  galvanized  iron  telegraph-wire  up  all  the  corners,  along  all 
the  ridges  and  eaves,   and  over  all  the  chimneys ;    taking  them 
down  to  the  earth  in  several  places,  to  a  moist  stratum,  and  at 
each  place  burying  a  load  of  coke. 

9.  Over  the  tops  of  tall  chimneys  it  is  well  to  place  a  loop  or 
arch  of  the  lightning  conductor,  made  of  any  stout  and  durable 
metal. 

357.  Steady  Strain  and  Impulsive  Rush.  —  Sir  Oliver 
Lodge  distinguishes  between  two  separate  cases  which  may 

arise.  If  a  thunder-cloud  ex- 
tending over  part  of  the  earth 
becomes  gradually  charged, 
or  if  a  charged  cloud  gradually 

FIG.  187.  -  Steady  Strain.  m°VeS   OV6r   a   Particular   SPOt, 

the  air  between  the  cloud  and 

the  earth  experiences  a  steadily  increasing  electric  stress, 
under  which  points  will  tend  to  discharge  better  than  blunt 
objects ;  and  they  are  more  likely  to  receive  the  lightning 
spark  when  it  occurs ;  hence  in  this  case  pointed  rods  best  pro- 
tect chimneys  of  given  height.  But  if  a  cloud  is  suddenly 
charged  by  receiving  a  lightning  spark  from  another  cloud  in 
a  sort  of  impulsive  rush,  a  pointed  rod  under  it  has  had  no 
chance  of  any  preparatory  action,  and  is  no  more  likely  to 
take  the  discharge  than  a  blunt  conductor  or  a  chimney- 
stack  of  equal  height. 

These  two  cases  may  be  imitated  in  the  laboratory  by 
arranging  apparatus  as  in  Figs.  187  and  188;  the  former 
of  which  illustrates  steady  strain,  the  latter  impulsive  rush. 
A  large  flat  sheet  of  metal  C  is  placed  to  represent  a  cloud, 


CH.  iv.  358]        ATMOSPHERIC   ELECTRICITY  317 

and  an  influence  machine  is  used  to  charge  the  Leyden  jars, 
as  shown.  If  three  objects  of  adjustable  height,  one  pointed, 
one  tipped  with  a  large  metal  ball,  and  one  tipped  with  a 
small  ball  are  placed  below  the  plate  C,  then  in  the  case  of 
steady  strain  it  is  found  that 
at  equal  heights  the  pointed 
conductor  is  more  liable  to 
be  struck,  and  it  may  be 
lowered  some  distance  before 
the  blunt  conductors  are 

11          f.  i      *         ,1  FIG.  188.  —  Impulsive  Rush. 

equally  often  struck  by  the 

discharge.  In  the  case  of  impulsive  rush,  which  occurs 
whenever  a  spark  passes  at  A,  causing  C  to  be  suddenly 
charged,  the  discharge  from  C  occurs  equally  often  when  all 
three  conductors  are  arranged  at  equal  heights. 

358.  Atmospheric  Electricity.  —  In  1752  Lemonnier  ob- 
served that  the  atmosphere  was  usually  in  an  electrified 
condition.  Cavallo,  Beccaria,  Ceca,  and  more  recently 
Quetelet  and  Lord  Kelvin  and  others,  added  to  our  knowledge 
of  the  subject.  The  main  result  is  that  the  air  above  the 
surface  of  the  earth  is  usually,  during  fine  weather,  posi- 
tively electrified,  or  at  least  that  it  is  positive  with  respect 
to  the  earth's  surface,  the  earth's  surface  being  relatively 
negative.  The  so-called  measurements  of  "  atmospheric 
electricity  "  are  really  measurements  of  difference  of  poten- 
tial between  a  point  of  the  earth's  surface,  and  a  point 
somewhere  in  the  air  above  it.  In  the  upper  regions  of  the 
atmosphere  the  air  is  highly  rarefied,  and  conducts  like 
the  rarefied  gases  in  Geissler's  tubes  (Art.  342).  The  lower 
air  is,  when  dry,  a  non-conductor.  The  upper  stratum  is 
believed  to  be  charged  with  +  electricity,  while  the  earth's 
surface  is  itself  negatively  charged;  the  stratum  of  denser 
air  between  acting  like  the  glass  of  a  Leyden  jar  in  keeping 
the  opposite  charges  separate.  If  we  could  measure  the 
electric  potential  at  different  points  within  the  thickness  of 
the  glass  of  a  charged  jar,  we  should  find  that  the  values  of 


318  ELECTRICITY   AND   MAGNETISM      [PT.  H.  359 

the  potential  changed  in  regular  order  from  a  -f-  value  at 
one  side  to  a  —  value  at  the  other,  there  being  a  point  of 
zero  potential  about  halfway  between  the  two.  Now,  the 
air  in  fine  weather  always  gives  +  indications,  and  the  poten- 
tial of  it  is  higher  the  higher  we  go  to  measure  it.  Cavallo 
found  higher  electrification  just  outside  the  cupola  of  St. 
Paul's  Cathedral  than  at  a  lower  point  of  the  building. 
Lord  Kelvin  found  the  potential  in  the  island  of  Arran  to 
increase  from  23  to  46  volts  for  a  rise  of  one  foot  in  level; 
but  the  difference  of  potential  was  sometimes  eight  or  ten 
times  as  much  for  the  same  difference  of  level,  and  changed 
rapidly,  as  the  east  wind  blew  masses  of  cloud  charged  with 
+  or  —  electricity  across  the  sky.  Joule  and  Kelvin,  at 
Aberdeen,  found  the  rise  of  potential  to  be  equal  to  40  volts 
per  foot,  or  1-3  volts  per  centimetre  rise  of  level. 

During  fine  weather  a  negative  electrification  of  the  air  is 
extremely  rare.  Beccaria  only  observed  it  six  times  in 
fifteen  years,  and  then  with  accompanying  winds.  But  in 
broken  weather  and  during  rain  it  is  more  often  —  than  -f-, 
and  exhibits  great  fluctuations,  changing  from  —  to  +,  and 
back,  several  times  in  half  an  hour.  A  definite  change  in 
the  electrical  conditions  usually  accompanies  a  change  of 
weather.  "  If,  when  the  rain  has  ceased  [said  Ceca],  a  strong 
excessive  ( +)  electricity  obtains,  it  is  a  sign  that  the  weather 
will  continue  fair  for  several  days." 

359.  Methods  of  Observation.  —  The  older  observers 
were  content  to  affix  to  an  electroscope  (with  gold  leaves  or 
pith-balls)  an  insulated  pointed  rod  stretching  out  into  the 
air  above  the  ground,  or  to  fly  a  kite,  or  (as  Becquerel  did) 
to  shoot  into  the  air  an  arrow  communicating  with  an  elec- 
troscope by  a  fine  wire,  which  was  removed  before  the  arrow 
fell.  Gay-Lussac  and  Biot  lowered  a  wire  from  a  balloon, 
and  found  a  difference  of  potential  between  the  upper  and 
lower  strata  of  the  air.  None  of  these  methods  is  quite 
satisfactory,  for  they  do  not  indicate  the  potential  at  any 
one  point.  To  bring  the  tip  of  a  rod  to  the  same  potential 


CH.  iv.  360]         ATMOSPHERIC  ELECTRICITY 

as  the  surrounding  air,  it  is  necessary  that  material  particles 
should  be  discharged  from  that  point  for  a  short  time,  each 
particle  as  it  breaks  away  carrying  with  it  a  +  or  a  —  charge 
until  the  potentials  are  equalized  between  the  rod  and  the 
air  at  that  point.  Volta  did  this  by  means  of  a  small  flame 
at  the  end  of  an  exploring  rod.  Lord  Kelvin  employed  a 
"  water-dropper,"  that  is  an  insulated  cistern  provided  with 
a  nozzle  protruding  into  the  air,  from  which  drops  issue  to 
equalize  the  potentials :  in  winter  he  uses  a  small  roll  of 
smouldering  touch-paper.  Dellmann  adopted  another 
method,  exposing  a  sphere  to  influence  by  the  air,  and  then 
insulating  it,  and  bringing  it  within-doors  to  examine  its 
charge.  Peltier  adopted  the  kindred  expedient  of  placing, 
on  or  near  the  ground,  a  delicate  repulsion-electrometer, 
which  during  exposure  was  connected  to  the  ground,  then 
insulated,  then  removed  indoors  for  examination.  This 
process  really  amounted  to  charging  the  electrometer  by 
influence  with  electrification  of  opposite  sign  to  that  of  the 
air.  The  "  quadrant  "  electrometer,  described  in  Art.  307, 
and  a  "  portable  "  electrometer  on  the  attracted-disk  prin- 
ciple, are  now  used  for  observations  on  atmospheric  elec- 
tricity. Using  a  water-dropping  collector  and  a  Kelvin 
electrometer,  Everett  made  a  series  of  observations  in  Nova 
Scotia,  and  found  the  highest  -h  electrification  in  frosty 
weather,  with  a  dry  wind  charged  with  particles  of  ice. 

360.  Diurnal  Variations.  —  Quetelet  found  that  at  Brus- 
sels the  daily  indications  (during  fine  weather)  showed  two 
maxima  occurring  in  summer  at  8  A.M.  and  9  P.M.,  and  in 
winter  at  10  A.M.  and  6  P.M.  respectively,  and  two  minima 
which  in  summer  were  at  the  hours  of  3  P.M.  and  about  mid- 
night. He  also  found  that  in  January  the  electricity  was 
about  thirteen  times  as  strong  as  in  June.  At  Kew  there 
is  a  maximum  at  8  A.M.  in  summer,  and  at  10  A.M.  in  winter ; 
and  a  second  minimum  at  10  P.M.  in  summer  and  7  P.M.  in 
winter.  The  maxima  correspond  fairly  with  hours  of  chang- 
ing temperature,  the  minima  with  those  of  constant  tern- 


320 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  361 


perature.  In  Paris,  Mascart  found  but  one  maximum,  just 
before  midnight :  at  sunrise  the  electricity  diminishes  until 
about  3  P.M.,  when  it  has  reached  a  minimum,  whence  it 
rises  till  nightfall.  Our  knowledge  of  this  important  sub- 
ject is  still  very  imperfect.  We  do  not  even  know  whether 
all  the  changes  of  the  earth's  electrification  relatively  to  the 
air  are  due  to  causes  operating  above  or  below  the  earth's 
surface. 

361.    The  Aurora.  —  In  all  the  northern  regions   of  the 
earth  the  Aurora  borealis,  or  "  Northern  Lights,"  is  an  occa- 


FIG.  189.  —  The  Aurora  Borealis. 

sional  phenomenon ;  and  within  and  near  the  Arctic  circle 
is  of  almost  nightly  occurrence.  Similar  lights  are  seen  in 
the  south  polar  regions  of  the  earth,  and  are  denominated 
Aurora  australis.  As  seen  in  European  latitudes,  the  usual 
form  assumed  by  the  aurora  is  that  of  a  number  of  ill-defined 
streaks  or  streamers  of  a  pale  tint  (sometimes  tinged  with 
red  and  other  colours),  either  radiating  in  a  fan-like  form 


CH.  iv.  361]  THE   AURORA  321 

from  the  horizon  in  the  direction  of  the  (magnetic)  north,  or 
forming  a  sort  of  arch  across  that  region  of  the  sky,  of  the 
general  form  shown  in  Fig.  189.  A  certain  flickering  or 
streaming  motion  is  often  discernible  in  the  streaks.  Under 
very  favourable  circumstances  the  aurora  extends  over  the 
en  tire- sky.  The  appearance  of  an  aurora  is  usually  accom- 
panied by  Si  magnetic  storm  (Art.  166),  causing  the  compass- 
needles  over  whole  regions  of  the  globe  to  be  disturbed  with 
irregular  and  repeated  deviations.  This  fact,  and  the  posi- 
tion of  the  auroral  arches  and  streamers  with  respect  to  the 
magnetic  meridian,  directly  suggest  an  electric  origin  for 
the  light,  —  a  conjecture  which  is  confirmed  by  the  many 
analogies  found  between  auroral  phenomena  and  those  of 
discharge  in  rarefied  air  (Arts.  342  and  345).  Yet  the 
presence  of  an  aurora  does  not,  at  least  in  our  latitudes, 
affect  the  electrical  conditions  of  the  lower  regions  of  the 
atmosphere.  On  September  1,  1859,  a  severe  magnetic 
storm  occurred,  and  aurorae  were  observed  almost  all  over 
the  globe ;  at  the  same  time  a  remarkable  outburst  of  energy 
took  place  in  the  photosphere  of  the  sun;  but  no  simul- 
taneous development  of  atmospheric  electricity  was  recorded. 
Aurorse  appear  in  greater  frequency  in  periods  of  about  11§ 
years,  which  agrees  pretty  well  with  the  cycles  of  maximum 
of  magnetic  storms  (see  Art.  166)  and  of  sun-spots. 

The  spectroscope  shows  the  auroral  light  to  be  due  to 
gaseous  matter,  its  spectrum  consisting  of  a  few  bright  lines 
apparently  characteristic  of  the  rarer  gases  lately  discovered 
as  constituents  of  the  atmosphere. 

According  to  Nordenskiold  the  terrestrial  globe  is  per- 
petually surrounded  at  the  poles  with  a  ring  or  crown  of 
light,  single  or  double,  to  which  he  gives  the  name  of  the 
"  aurora-glory."  The  outer  edge  of  this  ring  he  estimates 
to  be  at  120  miles  above  the  earth's  surface,  and  its  diameter 
about  1250  miles.  The  centre  of  the  aurora-glory  is  not 
quite  at  the  magnetic  pole,  being  in  lat.  81°  N.,  long.  80°  E. 
This  aurora-glory  usually  appears  as  a  pale  arc  of  light  across 


322  ELECTRICITY   AND   MAGNETISM     [PT.  n.  361 

the  sky,  and,  except  during  magnetic  and  auroral  storms,  is 
destitute  of  the  radiating  streaks  shown  in  Fig.  189. 

An  artificial  aurora  was  produced  by  Lemstrom,  who 
erected  on  a  mountain  in  Lapland  a  network  of  wires  pre- 
senting many  points  to  the  sky.  By  insulating  this  appa- 
ratus and  connecting  it  by  a  telegraph-wire  with  a  galvanom- 
eter at  the  bottom  of  the  mountain,  he  was  able  to  observe 
actual  currents  of  electricity  when  the  auroral  beam  appeared 
above  the  mountain.  Birkeland  has  reproduced  the  auroral 
corona  experimentally  by  sending  electric  discharges  into  a 
large  partially  exhausted  vacuum  tube  in  which  was  sus- 
pended a  spherical  electromagnet  as  a  model  of  the  earth's 
globe. 

The  electron  theory  has  been  made  by  Arrhenius  to  ac- 
count for  the  occurrence  of  aurorae  and  the  allied  phe- 
nomena of  magnetic  storms  and  the  solar  corona. 

The  sun  is  regarded  as  continually  discharging  electrons 
into  space.  In  the  approximate  vacuum  immediately  sur- 
rounding the  sun  the  flying  electrons  may  well  give  rise  to 
the  appearance  of  the  solar  corona.  The  earth  is  exposed 
to  a  continual  bombardment  of  electrons  from  the  sun,  and 
the  aurorae  are  due  to  the  catching  and  guiding  of  the 
streams  of  electrons  by  the  earth's  magnetic  lines  of  force 
directed  to  the  poles,  where  in  the  rarefied  upper  regions  of 
the  atmosphere  the  phenomena  of  the  vacuum  tube  are 
reproduced.  A  torrent  of  electrons  constitutes  an  electric 
current  of  strength  sufficient  to  produce  considerable  mag- 
netic effects,  and  thus  the  connexion  of  aurorae  and  mag- 
netic storms  is  explained. 


CHAPTER  V 

ELECTROMAGNETICS 

LESSON  XXVI.  —  Magnetic  Potential 

362.  Electromagnetics.  —  That  branch  of  the  science  of 
electricity  which  treats  of  the  relation  between  electric  cur- 
rents and  magnetism  is  termed  Electromagnetics.  In  Arts. 
130  to  142  the  laws  of  magnetic  forces  were  explained,  and 
the  definition  of  "  unit  pole  "  was  given.  It  is,  however, 
much  more  convenient,  for  the  purpose  of  study,  to  express 
the  interaction  of  magnetic  and  electromagnetic  systems  in 
terms  not  of  "  force  "  but  of  "  potential ";  i.e.  in  terms  of 
their  power  to  do  work.  In  Art.  280  the  student  was  shown 
how  the  electric  potential  due  to  a  quantity  of  electricity 
may  be  evaluated  in  terms  of  the  work  done  in  bringing  up 
as  a  test  charge  a  unit  of  +  electricity  from  an  infinite  dis- 
tance. Magnetic  Potential  can  be  measured  similarly  by 
the  ideal  process  of  bringing  up  a  unit  magnetic  pole  (N- 
seeking)  from  an  infinite  distance,  and  ascertaining  the 
amount  of  work  done  in  the  operation.  Hence  a  large  num- 
ber of  the  points  proved  in  Lesson  XXI.  concerning  electric 
potential  will  also  hold  true  for  magnetic  potential.  The 
student  may  compare  the  following  propositions  with  the 
corresponding  ones  in  Articles  280  to  285 :  — 

(a)  The  magnetic  potential  at  any  point  is  the  work  that 
must  be  spent  upon  a  unit  magnetic  (N-seeking)  pole 
in  bringing  it  up  to  that  point  from  an  infinite  dis- 
tance. 

(b)  The  magnetic  potential  at  any  point  due  to  a  system 

323 


324  ELECTRICITY  AND   MAGNETISM     [PT.  n.  362 

of  magnetic  poles  is  the  sum  of  the  separate  magnetic 
potentials  due  to  the  separate  poles. 

The  student  must  here  remember  that  the  potentials  due 
to  S-seeking  poles  will  be  of  opposite  sign  to  those  due  to 
N-seeking  poles,  and  must  be  reckoned  as  negative. 

(c)  The  (magnetic)'  potential  at  any  point  due  to  a  system 
of  magnetic  poles  may  be  calculated  (compare  with 
Art.  280)  by  summing  up  the  strengths  of  the  separate 
poles  divided  each  by  its  own  distance  from  that  point. 
Thus,  if  poles  of  strengths  m',  m"  ',  ra'",  etc.,  be 
respectively  at  distances  of  r',  r",  r'ff,  .  .  ,  from 
a  point  P,  then  the  following  equation  gives  the 
potential  P  :  — 


v    _m       m 
Vp~  r       T^ 


(d)  The  difference  of  (magnetic)   potential  between   two 
points  is  the  work  to  be  done  on  or  by  a  unit  (N-seek- 
ing) pole  in  moving  it  from  one  point  to  the  other.     It 
follows  that  if  m  units  of  magnetism  are   moved 
through  a  difference  of  potential  V,  the  work  W  done 
will  be 

W  =  mV. 

(e)  Magnetic  force  on  unit  pole  is  the  rate  of  change  of 
(magnetic)  potential  per  unit  of  length :  it  is  numeri- 
cally equal  to  the  intensity  of  the  field.     This  is 
proved  thus  :  —  In  Art.  142,  §,  the  intensity  of  the 
field  is  defined  by  the  force  exerted  by  the  field  on  a 
unit  of  magnetism,  it  follows  that  on  m  units   of 
magnetism  the  force  /  will  be  m  times  as  great,  or, 


CH.  v.  362]  MAGNETIC   POTENTIAL  325 

Now  work  is  the  product  of  a  force  into  the  length 
through  which  its  point  of  application  moves  for- 
ward ;  hence  it  follows  that 


But 

W  =  mV; 
whence 

V  =&, 
and 

©  -  V/l. 

§,   at  any  point,  is  therefore  the  same   as  the  potential 
gradient  at  that  point. 

Example.  —  The  difference  of  magnetic  potential  between  two 
points  5  centims.  apart  along  a  magnetic  field  in  which 
there  are  6000  lines  per  sq.  cm.,  is  30,000.  Or,  it  would 
require  30,000  ergs  of  work  to  be  expended  to  push  a 
unit  pole  from  one  point  to  the  other  against  the  magnetic 
force. 

(f)  Equipotential  surfaces  are  those  (imaginary)  surfaces 
surrounding  a  magnetic  pole  or  system  of  poles,  over 
which  the  (magnetic)  potential  has  equal  values. 
Thus,  around  a  single  isolated  magnetic  pole,  the 
potential  would  be  equal  all  round  at  equal  dis- 
tances; and  the  equipotential  surfaces  would  be  a 
system  of  concentric  spheres  at  such  distances  apart 
that  it  would  require  the  expenditure  of  one  erg  of 
work  to  move  a  unit  pole  up  from  a  point  on  the 
surface  of  one  sphere  to  any  point  on  the  next  (see 
Fig.  160).  Around  any  real  magnet  possessing  two 
polar  regions  the  equipotential  surfaces  would  become 
much  more  complicated.  Magnetic  force,  whether  of 
attraction  or  repulsion,  always  acts  across  the  equipoten- 
tial surfaces  in  a  direction  normal  to  the  surface;  the 
magnetic  lines  of  force  are  everywhere  perpendicular  to 
the  equipotential  surfaces. 


326          ELECTRICITY   AND   MAGNETISM    [FT.  n.  363,  364 

363.  Magnetic   Tubes   of  Force.  —  From  a  single  mag- 
netic pole  (supposed  to  be  a  point  far  removed  from  all  other 
poles)  the  lines  of  force  diverge  radially  in  all  directions. 
The  space  around  may  be  conceived  as  thus  divided  up  into 
a  number  of  conical  regions,  each  having  its  apex  at  that 
pole;   and  through  each  cone,  as  through  a  tube,  a  certain 
number  of  lines  of  force  will  pass.     Such  a  conical  space 
may  be  called  a  tube  of  force.     The  total  number  of  magnetic 
lines  within  any  tube  of  force  is  called  the  magnetic  flux.1 
No  matter  where  you  cut  across  a  tube  of  force,  the  cross- 
section  will  cut  through  the  enclosed  flux,  though  the  lines 
diverge  more  widely  as  the  tube  widens.     Hence, 

(g)  The  magnetic  flux  across  any  section  of  a  tube  of  force 
is  constant  wherever  the  section  be  taken. 

In  case  the  magnetism  is  not  concentrated  at  one  point, 
but  distributed  over  a  surface  from  which  the  tubes  start, 
we  shall  have  to  speak  of  the  "  amount  of  magnetism  " 
rather  than  of  the  "  strength  of  pole,"  and  in  such  a  case  the 

(h)  Magnetic  density  is  the  amount  of  magnetism  per  unit 
of  surface.  In  the  case  of  a  simple  magnetic  shell 
over  the  face  of  which  the  magnetism  is  distributed 
with  uniform  density,  the  "  strength  "  of  the  shell  is 
defined  as  the  thickness  of  the  shell  multiplied  by 
the  surface-density. 

364.  Magnetic    Flux.  —  The    term    magnetic    flux,    used 
above,  receives  a  special  significance  when  we  consider  mag- 
netic circuits,  that  is  to  say,  systems  (such  as  electromagnets 
with   their  keepers)    wherein   the   magnetic   lines   traverse 
definite  paths  in  a  circuital  manner,  and  thread  their  way 
through  the  magnetizing  coil  which  surrounds  them.     The 
magnetic  flux  denotes  the  total  number  of  such  magnetic 
lines  following  the  course  of  the  circuit.     The  whole  num- 

1  The  magnetic  flux  is  by  some  writers  called  the  total  induction;  but 
the  word  induction  ought  to  be  kept  for  the  operation  of  inducing. 


CH.  v.  365]  INTENSITY   OF   FIELD  327 

ber  of  lines  in  the  flux  of  a  large  electromagnet  may  amount 
to  several  millions,  depending  on  the  cross-section  of  the 
iron  core,  and  the  degree  to  which  it  is  magnetized.  The 
amount  of  flux  divided  by  the  cross-section  of  the  circuit  is 
called  the  flux-density  (symbol  33)  .  If  a  flux  of  g  lines  passes 
through  area  A,  the  flux-density  will  be 


Example.  —  In  a  certain  electromagnet  the  core  of  which  had  a 
cross-section  of  72  square  centimetres,  the  magnetic  flux 
was  found  to  be  1,188,000  lines.  The  flux-density  in  the 
iron  was  therefore  16,500  lines  per  square  centimetre. 

365.  Intensity  of  Field.  —  We  have  seen  (Art.  118)  that 
every  magnet  is  surrounded  by  a  certain  "  field,"  within 
which  magnetic  force  is  observable.  We  may  completely 
specify  the  properties  of  the  field  at  any  point  by  measur- 
ing, the  strength  and  the  direction  of  that  force,  —  that  is,  by 
measuring  the  "  intensity  of  the  field  "  and  the  direction  of 
the  lines  of  force.  The  "  intensity  of  the  field  "  at  any  point 
is  measured  by  the  force  with  which  it  acts  on  a  unit  pole  placed 
at  that  point.  Hence,  unit  intensity  of  field  is  that  intensity 
of  field  which  acts  on  a  unit  pole  with  a  force  of  one  dyne. 
There  is  therefore  a  field  of  unit  intensity  at  a  point  one 
centimetre  distant  from  the  pole  of  a  magnet  of  unit  strength. 
Suppose  a  magnet  pole,  whose  strength  is  m,  placed  in  a 
field  at  a  point  where  the  intensity  is  §,  then  the  force  will 
be  m  times  as  great  as  if  the  pole  were  of  unit  strength,  and 

/  =  m  X  §• 

To  aid  the  imagination  by  a  graphic  conception  we  adopt 
Faraday's  notion  of  representing  the  properties  of  a  magnetic 
field  by  supposing  lines  to  be  drawn  so  that  they  represent 
the  direction  and  intensity  of  the  field  by  the  direction  and 
density  of  the  lines.  This  leads  to  the  empirical  rule  to 
draw  as  many  magnetic  lines  to  the  square  centimetre  (of 
cross  section)  as  there  would  be  dynes  of  force  on  unit  pole. 


328          ELECTRICITY   AND   MAGNETISM    [PT.  n.  366,  367 

A  field  of  §  units  means  one  where  there  would  be  §  dynes 
on  unit  pole,  or  §  lines  per  square  centimetre.  It  follows 
that  a  unit  magnetic  pole  will  have  a  flux  of  4  TT  lines  proceed- 
ing from  it;  for  there  is  unit  field  at  unit  distance  away,  or 
one  magnetic  line  per  square  centimetre ;  and  there  are  4  TT 
square  centimetres  of  surface  on  a  sphere  of  unit  radius 
drawn  round  the  pole.  A  magnet,  whose  pole-strength  is  m, 
has  a  flux  of  47rra,  or  12-57  X  m,  lines  running  through  the 
steel,  and  diverging  at  its  pole.  This  is  the  origin  of  the  4  TT 
symbol  which  comes  in  so  often  into  electromagnetic  formulae. 
Suppose  a  narrow  crevasse  between  the  faces  of  two  opposing 
magnets,  each  having  a-  units  of  magnetism  per  square 
centimetre  of  their  pole  surfaces.  The  field  in  the  space 
between  will  have  the  value 

©  =  4  TTO-. 

366.  Work  done  by  Conductor  carrying  Current  when  it 
cuts  across  the  Lines  of  a  Magnetic  Field.  —  By  definition 
(Art.  280)  it  follows  that  the  work  W  done  in  moving  Q 
units  of  electricity  against  an  electromotive-force  V  is  equal 
to  QV.     Suppose  that  this  electromotive-force  is  due  to  the 
conductor  cutting  g  magnetic  lines  during  time  t.     Then  if 
the  motion  be  uniform  and  the  average  current  during  the 
time  is  called  i}  it  follows  that  Q  =  it.     And  the  average 
electromotive-force  is  (see  Art.  243)  =  $/t.     Inserting  these 
values  we  get 

W  =  it  X  g/«, 
or  W  =  tg  ; 

or,  in  words,  the  work  done  in  moving  a  curent  across  a  mag- 
netic flux  is  equal  to  the  product  of  the  current  into  the  total 
number  of  magnetic  lines  cut.  It  will  be  noted  that  the  work 
done  is  the  same  whether  the  time  is  long  or  short.  If  i  and 
g  are  in  absolute  (C.G.S.)  units,  W  will  be  in  ergs. 

367.  Force  exerted  by  Magnetic  Field  on  Wire  carrying 
Current.  —  If  a  wire  is  moved  sideways  across  the  lines  of  a 


CH.  v.  367     FORCE   EXERTED   ON  A   CONDUCTOR       329 


magnetic  field,  through  a  distance  x,  it  will  sweep  out  an 
area  equal  to  its  own  length  I  multiplied  by  x.  And  if  § 
is  the  number  of  magnetic  lines  per  square  centimetre  the 
total  number  of  lines  cut  will  be  =  &lx ;  and  the  work  done 
if  the  wire  carries  current  i  will  be  W  =  ifelx.  But  if  work 
W  is  done  in  moving  the  wire  through  distance  x  the  force  / 
exerted  will  be  W/x.  Hence 
the  force,  in  dynes,  on  the  wire 
will  be 

/  = 


or,  in  words,  the  force  is  pro- 
portional to  the  current,  to  the 
intensity  of  the  field,  and  to 
the  length  of  wire  in  the  field. 
It  is  a  force  l  that  tends  to 
drag  the  wire  laterally,  acting 
at  right  angles  to  the  wire  and 
to  the  lines  of  the  field. 

This  action  is  of  course  due 
to  stresses  going  on  in  the 
medium,  and  is  worthy  of 

further  thought.  Consider  the  magnetic  field  in  a  gap  be- 
tween a  large  N-pole  and  a  similar  S-pole.  The  lines  will  go 
nearly  uniformly  straight  across.  Let  a  current  flow  in  a 
copper  wire  that  lies  across  the  field.  In  Fig.  190  the  wire 
is  seen  endways,  with  the  current  flowing  "  up  "  or  toward 
the  observer.  The  result  will  be  that  the  magnetic  field  of 
the  current  (Arts.  215  and  370)  will  be  superposed  (Art.  144) 
upon  that  of  the  magnets,  and  will  perturb  it :  the  form  of 
the  perturbed  field  being  that  shown.  In  such  a  field  the 
stresses,  which  act  as  though  the  magnetic  lines  tended  to 
shorten  themselves,  will  have  the  effect  of  urging  the  wire 
mechanically  in  the  direction  shown.  This  mechanical  force 
acts  on  the  matter  of  the  wire,  though  due  to  the  current. 

1  In  calculating  by  the  expression  above,  if  i  is  given  in  amperes  it  must 
be  divided  by  10. 


330  ELECTRICITY   AND   MAGNETISM      [PT.  n.  368 

368.  Magnetomotive-force  (or  Total  Magnetizing  Force) 
of  a  Current  circulating  in  a  Spiral  Conductor.  —  Let  a  con- 
ductor carrying  a  current  of  i  amperes  be  coiled  up  in  a 
spiral  having  S  as  the  number  of  turns.  It  is  known,  and 
easily  understood,  that  the  total  magnetizing  force  of  such  is 
proportional  to  the  number  of  ampere-turns  ;  for  experiment 
shows  that,  for  example,  a  current  of  10  amperes  circulating 
in  a  coil  of  50  turns  has  precisely  the  same  magnetic  power 
as  a  current  of  5  amperes  in  100  turns,  or  as  a  current  of  1 
ampere  in  500  turns.  Each  of  these  has  500  ampere-turns. 

To  obtain  the  full  expression  let  us  find  the  work  that 
would  be  done  in  the  act  of  moving  a  unit  magnet-pole 
around  any  closed  path  (Fig.  191)  from  any 
point  P  to  the  same  point  again,  such  path 


)    passing  through  all  the  turns  of  the  magnetiz- 
Fj'J'igi"         ing  coil.     The  work  done  on  a  unit-pole  in 
moving  it  once  around  the  closed  path,  against 
the  magnetic  forces  of  the  system,  is  a  measure  of  the  ability 
of  that  system  to  magnetize;  or,  in  other  words,  is  a  measure 
of  its  magnetomotive-force.1     Such  a  closed  path  may  lie, 
according  to  circumstances,  either  wholly  in  air,  or  partly  in 
air  partly  in  iron,  or  wholly  in  iron.     The  argument  is  entirely 
independent  of  any  materials  lying  along  the  ideal  path. 

Now  imagine  this  unit-pole,  with  its  4?r  magnetic  lines 
radiating  out  of  it,  to  be  passed  along  the  closed  path  (Fig. 
191)  from  P,  through  the  spirals  to  P  again.  Each  turn  of 
the  coil  will  cut  each  of  the  magnetic  lines  once,  and  there- 
fore, by  Arts.  365  and  366,  the  total  work  done  will  be 

W  =  4iriS/W, 

where  we  divide  by  10  to  bring  amperes  to  absolute  C.G.S. 
units.  Hence  the  magnetomotive-force  of  that  coil  is  pro- 
portional to  the  number  of  ampere-turns. 

1  Since  this  magnetomotive-force  is  made  up  of  a  number  of  small  elements 
distributed  variously  along  the  path,  it  is  sometimes  called  the  line-integral 
of  the  magnetizing  forces. 


CH.  v.  369,  370]    FIELD   DUE    TO   CURRENT  331 

369.  Intensity  of  Field  in  a  long  Tubular  Coil    or  Sole- 
noid. —  A  spiral  coil  wound  on  a  tube  is  called  a  solenoid. 
It  has,  when  a  current  circulates  in  its  coils,  a  magnetic 
field  along  the  inside  of  it,  and  is,  in  fact,  so  long  as  the 
current  circulates,  a  magnet  without  iron.     This  magnetic 
field,  if  the  spiral  is  a  very  long  one  —  say  20  times  as  long 
as  the  diameter  of  the  spirals,  —  is  very  uniform  all  along 
the  interior,  except  just  toward  the  ends,  where  it  becomes 
weaker.     To  find  the  intensity  of  the  field  §,  we  may  re- 
member that  (Art.  362,  e)  the  work  done  on  a  unit-pole  in 
moving  it  through  a  length  I  of  field  §  is  equal  to  §L     But 
the  work  done  in  moving  it  along  the  tubular  coil  of  length 
Z  is  practically  equal  to  that  done  around  the  closed  path, 
since  nearly  all  the  forces  are  met  along  the  part  of  the  path 
inside.     Hence  we  may  equate  4  iriS/W  to  §Z;  giving  the 
result 

~  (.  N      4  TT  .  .  iS 

§  (in  gausses)  =  —  X  y> 

or  the  intensity  of  the  field  in  a  long  spiral  is  equal  to  1  -257 
times  the  number  of  ampere-turns  per  centimetre  of  length. 

At  the  mouth  of  a  long  spiral  the  intensity  of  the  field  is 
exactly  half  what  it  is  midway  between  the  ends. 

Example.  —  A  tubular  coil  60  cm.  long  is  wound  with  8  layers 
of  280  turns  each,  of  an  insulated  wire  carrying  4  amperes. 
The  value  of  §  all  along  the  middle  portion  of  the  coil 
will  be  187*5  gausses.  At  the  open  ends  the  value  will 
be  94  gausses. 

370.  Magnetic   Field   due   to   Indefinitely   Long   Straight 
Current.     Law  of  Inverse   Simple   Distance.  —  Consider  a 
unit-pole  at  point  P  at  a  distance  r  (Fig.  192)  from  an  in- 
definitely long  straight  conductor  carrying  a  current  of  i 
amperes.     The  force  tending  to   make   the  pole   circulate 
around  the  wire  may  be  calculated  very  simply  as  follows. 
If  the  unit-pole  were  to  be  moved  once  around  the  wire  on 
a  circular  path  with  radius  r,  each  one  of  the  4  TT  magnetic 


332 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  370 


lines  that  radiate  from  it  would  be  cut  once  by  the  wire. 

Hence,  by  Art.  366,  the  work  done  in  one  such  revolution 
would  be  equal  to  4  iri/W.  But  this  work  has  been 
done  by  moving  the  unit,  against  the  forces  of  the 
system,  along  a  path  the  length  of  which  is  2  irr ; 
wherefore 


whence 


f  =  2  i/Wr. 


FIG.  192.      From  this  it  appears  that  the  force  on  unit-pole, 
and  therefore  the  number  of  gausses  or  intensity 
of  the  field,  is  directly  proportional  to  the  current,  and  varies 
inversely  as  the  simple  distance  from  the  wire. 

Example.  —  The  force  exerted  on  a  pole  of  1200  units  of 
magnetism  at  a  distance  of  4  centimetres  from  a  long 
straight  wire  carrying  current  of  60  amperes  will  be  3600 
dynes,  or  3 '66  grammes. 

The  fact  that  the  force  varies  inversely  as  the  simple  dis- 
tance, and  not  as  the  square,  was  experimentally  discovered 
by  Biot  and  Savart  in  1820. 

Around  such  a  straight  con- 
ductor the  magnetic  field  consists 
of  a  cylindrical  whirl  of  circular 
lines  (Art.  215),  their  density  de- 
creasing as  their  radius  increases. 
Outside  a  straight  wire  carrying 
a  10-ampere  current  the  values  of 
§  are  :  2  at  1  cm. ;  1  at  2  cm.  ; 
0.4  at  5  cm.,  and  so  forth.  Fig. 
193  shows  the  falling  off  in  den- 
sity of  the  field  around  a  long 
straight  wire  carrying  a  current 

in  a  direction  downwards  normally  through  the  plane  of  the 
diagram.     A  pole  tends  to  move  circularly  around  the  wire. 


FIG.   193.  —  Field  surrounding  Cur- 
rent in  a  Straight  Wire. 


CH.  v.  371,  372]    FIELD   OF   CIRCULAR   COIL  333 

371.  Mutual  Action  of   Magnet-pole  and  of  Element  of 
Current.  —  Consider  an  element  of  current,  that  is  to  say, 
an  indefinitely  short  piece  of  a  con-  . 
ductor  traversed  by  a  current.     Call- 
ing the  length  dl,  and  the  current  i,    *g 

we  have  idl  as  the  magnetic  value  of  "^ 

the  element  with  respect  to  all  points 

in  its  equatorial  plane.     Suppose  the 

element  to  be  set  (Fig.  194)  at  distance  r  from  a  magnet-pole 

of  m  units,  and  at  right  angles  to  the  line  joining  them. 

Then,  as  the  element  is  small  compared  with  r,  the  law  of 

inverse  squares  will  hold  good  :  the  elementary  force  df  will  be 

m  •  idl 
=  ~10^' 

This  will  be  neither  an  attraction  nor  a  repulsion,  but  a 
force  at  right  angles  to  the  element  and  to  the  line  joining 
it  to  m.  If  the  elementary  conductor  is  oblique,  making  an 
angle  0  with  r',  the  expression  must  be  multiplied  by  sinO, 

makinSit:-  m-i-xind-dl 

10-f* 

372.  Magnetic    Field    due    to    Circular    Current.  —  It    is 
desired  to  find  the  effect  of  a  circular  current  (Fig.  195)  at 

any  point  on  the  axis,  at  a  distance  x  from 
the  centre.  Suppose  a  unit-pole  were 
placed  at  this  point  P,  only  a  fraction  of  the 
4  TT  lines  which  radiate  from  it  will  pass 
through  the  circle ;  the  number  being  pro- 
FIG.  195.  portional  to  the  solid-angle  (Art.  151)  sub- 

tended at  P  by  the  circle,  namely  2  w  (1 
—  cos  0),  where  0  is  the  angle  between  axis  and  slant  distance 
a.  Hence  in  bringing  up  the  pole  to  this  place,  from  an  in- 
finite distance,  the  work  done  by  causing  these  lines  to  cut 
across  the  wire  carrying  current  i  amperes  will  be  (by  Art.  366). 

W  =  2  7rt(l  -  cos  0)/10. 


]L 


334  ELECTRICITY   AND   MAGNETISM       [PT.  n.  372 

This  represents  the  mutual  energy  of  pole  and  current. 
To  calculate  the  force  at  P  we  must  differentiate  this 
expression  with  respect  to  x,  to  ascertain  the  rate  at  which 
the  mutual  energy  falls  per  unit  length.  For  this  purpose 
it  will  be  convenient  to  substitute  for  cos  0  its  value 
x/(x2  +  ?/2)*.  Substituting  and  differentiating  we  get 

/  =  dW/dx  =  T2¥  7riy2/(x*  +  i/2)i. 

Now  (x2  +  y2)%  is  equal  to  a3 ;  whence  the  rule  that  the 
magnetic  force  at  any  point  P  on  the  axis  varies  directly 
as  the  current,  and  inversely  as  the  cube  of  the  slant  distance. 
(Compare  case  of  a  bar-magnet,  Art.  140.) 

Another  way  of  arriving  at  this  result  is  as  follows. 
Taking  the  expression  found  in  Art.  371  for  the  action  of 
an  element  of  current,  we  may  consider  the  effect  of  the 
topmost  element  of  the  ring  (Fig.  195),  situated  at  a 
slant  distance  a  =  Vx2  -f  y2-  The  elementary  force  df 
exerted  on  unit-pole  at  P  by  the  element  idl  will  be  at 
right  angles  to  a  and  to  dl  (in  direction  of  the  arrow),  and, 
by  Art.  219,  of  the  value 

df  =  idl/10  a2. 

As  the  elements  such  as  dl  are  symmetrical  around  the  axis 
we  must  resolve  their  oblique  forces  into  two  parts :  part 
acting  at  right  angles  to  the  axis,  which  will  disappear  by 
mutually  cancelling  out  in  pairs,  and  part  acting  in  the  line 
of  the  axis,  which  will  for  each  element  be  equal  to  the  above 
expression  multiplied  by  sin  6.  So  that  the  elementary  axial 
force  due  to  each  element  of  length  dl  will  be 

df  =  idl  -  sin  0/10  a2 ; 
or,  since  sin  0  =  y/a, 

df  =  idl  -  y/W  a3. 

But  the  total  force  /  due  to  all  the  elements  will  be  the  inte- 
gral due  to  the  sum  of  their  lengths,  and  this  integral  length 


CH.  v.  373,  374]    MOMENT   OF   CIRCULAR   COIL  335 

around  the  circle  is  (id  =  2  iry.     Whence  it  at  once  follows 
that 


Example.  —  The  force  on  unit-pole  at  a  point  12  centimetres 
along  the  axis  from  the  centre  of  a  circle  of  wire  of  5 
centimetres  radius,  carrying  30  amperes  will  be  2  TT  X  30 
X  5  X  5  +  10  X  13  X  13  X  13  =  278  .  . 


Note  that  if  P  is  pushed  up  to  the  centre  of  the  circle 
a  =  y,  and  we  get  back  to  the  rule  for  the  tangent  galvanom- 
eter (Art,  225),  /  =  2  wi/10  r. 

Also  note  that  for  very  great  distances  of  P  from  centre  a 
becomes  sensibly  equal  to  x,  the  force  varying  inversely  as 
the  cube  of  the  axial  distance. 

This  affords  one  way  of  varying  the  sensitiveness  of  tangent 
galvanometers,  the  needle  with  its  scale  being  arranged  to 
slide  out  along  the  axis  of  the  coil.  At  a  point  P,  such  that 
a  =  2  y,  the  force  of  coil  on  needle  is  only  f  of  what  it  is  at 
centre. 

373.  Moment  of  Circular  Coil.  —  A  circular  coil  carrying 
a  current  acts  as  a  magnet  whose  axis  is  the  axis  of  the  coil. 
Its  magnetic  moment  (Art.  137)  will  be  the  product  of  the 
current  (in  absolute  units)  into  the  area  enclosed.     Or,  if 
i  is  in  amperes,  and  A  the  total  area  of  all  the  turns,  its  mo- 
ment will  be  Ai/W.     If  such  a  coil  is  placed  in  a  field  of  in- 
tensity §  it  will  tend  to  turn  so  as  to  place  its  axis  along  the 
direction  of  the  field.     If  the  angle  between  those  directions 
is  9,  the  torque  (or  turning-moment)  will  be  =  AiQ  sin  0/10. 

374.  Potential  due  to  a  Solenoidal  or  Circuital  Distribution  of 
Magnetism.  —  A  long  thin  uniformly  magnetized  magnet  exhibits 
poles  only  at  the  two  ends,  and  acts  on  external  objects  just  as  if 
there  were  two  equal  quantities  of  opposite  kinds  of  magnetism 
collected  at  these  two  points.     Such  a  distribution  of  magnetism 
is  sometimes  called  solenoidal  or  circuital.     The  magnetic  potential 
due  to  a  solenoid,  and  all  its  magnetic  effects,  depend  only  on  the 
position  of  its  two  poles,  and  on  their  strength,  and  not  on  the  form 
of  the  bar  between  them,  whether  straight  or  curved.     In  Art.  362 
(c)  was  given  the  rule  for  finding  the  potential  due  to  a  system  of 


336  ELECTRICITY  AND   MAGNETISM    [FT.  n.  375,  376 

poles.  Suppose  the  two  poles  of  a  solenoid  have  strengths  -f-  m 
and  —  m  respectively,  and  that  the  distances  of  these  poles  from 
an  external  point  P  are  rx  and  r2,  then  the  potential  at  P  will  be 


VP 


/I        1 
=  m  ( 

\n     r2 


Suppose  a  magnet  curled  round  until  its  N  and  S  poles  touch 
one  another :  it  will  not  act  as  a  magnet  on  an  external  object, 
and  will  have  no  "  field  "  ;  for  if  the  two  poles  are  in  contact,  their 
distances  n  and  r2  to  an  external  point  P  will  be  equal,  and 


-  -  -    will  be  =  0. 
r       rj 

375.  Potential    due    to    a    Magnetic    Shell.  —  Gauss    demon- 
strated that  the  potential  due  to  a  magnetic  shell  at  a  point  near  it 
is  equal  to  the  strength  of  the  shell  multiplied  by  the  solid-angle  sub- 
tended by  the  shell  at   that  point;    the  "  strength  "  of   a  magnetic 
shell  being  the  product  of  its  thickness  into  its  surface-density  of 
magnetization. 

If  w  represents  the  solid-angle  subtended  at  the  point  P,  and 
i  the  strength  of  the  shell,  then 

Vp  =  wi. 

Here  o>i  represents  the  work  that  would  have  to  be  done  on  or 
by  a  unit-pole,  to  bring  it  up  from  an  infinite  distance  to  the  point 
P,  where  the  shell  subtends  the  solid-angle  w. 
To  establish  this  proposition  would- require  the 
integral  calculus.  At  a  point  Q  where  the  solid- 
angle  subtended  by  the  shell  is  different,  the 
potential  will  be  different,  the  difference  of 
potential  between  P  and  Q  being 

VQ  —  VP   =  I(WQ  —  wP). 
FIG.  196. 

If  a  magnet-pole  whose  strength  is  m  were 

brought  up  to  P,  m  times  the  work  would  have  to  be  done,  or  the 
mutual  potential  would  be^  =  mui. 

376.  Potential  Energy  of  a  Magnet-pole  and  a  Shell.  —  It  is 
evident  that  if  the  shell  of  strength  i  is  to  be  placed  where  it  sub- 
tends a  solid-angle  w  at  the  pole  m,  it  would  require  the  expenditure 
of  the  same  amount  of  work  to  bring  up  the  shell  from  an  infinite 
distance  on  the  one  hand,  as  to  bring  up  the  magnet-pole  from 
an  infinite  distance  on  the  other ;  hence  mui  represents  both  the 


CH.  v.  376]    POTENTIAL  OF  MAGNETIC   SHELL  337 

potential  energy  of  the  pole  on  the  shell  and  the  potential  energy 
of  the  shell  on  the  pole.  Now  the  lines  of  force  from  a  pole  may 
be  regarded  as  proportional  in  number  to  the  strength  of  the  pole, 
and  from  a  single  pole  they  would  radiate  out  in  all  directions 
equally.  Therefore,  if  a  magnet-pole  was  placed  at  P,  at  the  apex 
of  the  solid-angle  of  a  cone,  the  number  of  lines  of  force  which  would 
pass  through  the  solid-angle  would  be  proportional  to  that  solid- 
angle.  It  is  therefore  convenient  to  regard  mw  as  representing 
the  number  of  lines  of  force  of  the  pole  which  pass  through  the  shell, 
and  we  may  call  the  number  so  intercepted  F.  Hence  the  potential 
energy  of  the  system  consisting  of  a  magnet-pole  and  a  magnetic  shell 
is  equal  to  the  strength  of  the  shell  multiplied  by  the  number  of  lines  of 
force  (due  to  the  magnet-pole)  which  pass  through  the  shell ;  or  W  =  Fi. 
To  bring  up  a  N-seeking  (or  +)  pole  against  the  repelling  force  of 
the  N-seeking  face  of  a  magnetic  shell  requires  a  positive  amount  of 
work  to  be  done ;  and  their  mutual  reaction  would  enable  work  to 
be  done  a£terwards  by  virtue  of  their  position :  in  this  case  then  the 
potential  is  +.  But  in  moving  a  N-seeking  pole  up  to  the  S-seeking 
face  of  a  shell  work  will  be  done  by  the  pole,  for  it  is  attracted  up ; 
and  the  work  done  by  the  pole  may  be  regarded  as  our  doing  nega- 
tive work. 

Again,  suppose  we  could  bring  up  a  unit  N-seeking  pole  against 
the  repulsion  of  the  N-seeking  face  of  a  shell  of  strength  i,  and 
should  push  it  right  up  to  the  shell ;  when  it  actually  reached  the 
plane  of  the  shell  the  shell  would  occupy  a  whole  horizon,  or  half 
the  whole  space  around  the  pole,  the  solid-angle1  it  subtended 
being  therefore  2  ?r,  and  the  potential  will  be  +  2  iri.  If  we  had 
begun  at  the  S-seeking  face  the  potential  at  that  face  would  be 
—  2  iri.  It  appears  then  that  the  potential  alters  its  value  by  4  i 
on  passing  from  one  side  of  the  shell  to  the  other. 

If  a  N-seeking  pole  be  brought  up  to  the  N-seeking  face  of  a  shell 
none  of  the  lines  of  force  of  the  magnet  will  cut  the  shell,  but  will 
be  repelled  out  as  in  Fig.  74 ;  whereas  if  a  N-seeking  pole*  be  brought 
up  to  the  S-seeking  face  of  a  shell,  large  numbers  of  the  lines  will 
be  run  into  one  another  as  in  Fig.  73 ;  and  the  pole,  as  a  matter  of 
fact,  will  be  attracted  up  to  the  shell,  where  as  many  lines  of  force 
as  possible  are  cut  by  the  shell.  We  may  formulate  this  action 
by  saying  that  a  magnetic  shell  and  a  magnet-pole  react  on  one 
another  and  urge  one  another  in  such  a  direction  as  to  make  the  num- 
ber of  lines  of  force  that  are  cut  by  the  shell  a  maximum  (Maxwell's 
Rule,  Art.  217).  Outside  the  attracting  face  of  the  shell  the  poten- 
tial is  —  wi ,  and  the  pole  moves  so  as  to  make  this  negative  quantity 

1  See  note  on  Ways  of  Reckoning  Angles,  Art.  147  and  Appendix  A. 


338  ELECTRICITY   AND   MAGNETISM      [PT.  n.  377 

as  great  as  possible,  or  to  make  the  potential  a  minimum.  Which 
is  but  another  way  of  putting  the  matter  as  a  particular  case  of  the 
general  proposition  that  bodies  tend  to  move  so  that  the  energy 
they  possess  in  virtue  of  their  position  tends  to  run  down  to  a 
minimum. 

377.  Magnetic  Potential  due  to  Current.  —  The  propositions 
concerning  magnetic  shells  given  in  the  preceding  paragraphs  derive 
their  great  importance  because  of  the  fact  laid  down  in  Art.  216 
that  circuits,  traversed  by  currents  of  electricity,  behave  like 
magnetic  shells.  Adopting  the  electromagnetic  unit  of  current 
(Art.  380),  we  may  at  once  go  back  to  Art.  374  and  take  the  theorems 
about  magnetic  shells  as  being  also  true  of  closed  voltaic  circuits. 

(a)  Potential  due  to  closed  circuit  (compare  Art.  375). 

The  potential  V  due  to  a  closed  voltaic  circuit  (traversed  by  a 
current)  at  a  point  P  near  it,  is  equal  to  the  strength  of  the  current 
multiplied  by  the  solid-angle  w  subtended  by  the  circuit  at  that  point. 
If  i  be  the  strength  of  the  current  in  absolute  electromagnetic  units, 
then 

VP  =  -  o>i. 

(6)  At  a  point  Q,  where  the  solid-angle  subtended  by  the  circuit 
is  WQ  instead  of  wp,  the  potential  will  have  a  different  value,  the 
difference  of  potential  being 

VQ  —  Vp  =  — 

(c)  Mutual  Potential  of  a  Magnet-pole  and  a  Circuit.  —  If  a 
magnet-pole  of  strength  m  were  brought  up  to  P,  ra  times  as  much 
work  will  be  done  as  if  the  magnet-pole  had  been  of  unit  strength, 
and  the  work  would  be  just  as  great  whether  the  pole  m  were 
brought  up  to  the  circuit  or  the  circuit  up  to  the  pole.  Hence,  the 
mutual  potential  energy  will  be 


But,  as  in  Art,  376,  we  may  regard  raw  as  representing  the  number 
of  lines  of  force  of  the  pole  which  are  intercepted  by  and  pass 
through  the  circuit,  and  we  may  write  F  for  that  number,  and  say 

V  =  -  *F, 

or  the  mutual  potential  energy  of  a  magnet-pole  and  a  circuit  is  equal 
to  the  strength  of  the  current  multiplied  by  the  number  of  the  magnet- 
pole's  lines  of  force  that  are  intercepted  by  the  circuit,  taken  with 
reversed  sign. 


CH.  v.  3781  MUTUAL  POTENTIAL  339 

(d)  As  in  the  case  of  the  magnetic  shell,  so  with  the  circuit, 
the  value  of  the  potential  changes  by  4iri  from  a  point  on  one 
side  of  the  circuit  to  a  point  just  on  the  other  side ;  that  is  to  say, 
being  —  2  iri  on  one  side  and  +  2  iri  on  the  other  side,  work  equal 
to  4  vi  must  be  done  in  carrying  a  unit-pole  from  one  side  to  the 
other  round  the  outside  of  the  circuit.  The  work  done  in  thus 
threading  the  circuit  along  the  path  looped  S  times  round  it  would 
be  4  TT  Si. 

378.  (e)  Mutual  Potential  of  two  Circuits.  —  Two  closed  circuits 
will  have  a  mutual  potential,  depending  on  the  strengths  of  their 
respective  currents,  on  their  distance  apart,  and  on  their  form  and 
position.  If  their  currents  be  respectively  i  and  i',  and  if  the  dis- 
tance between  two  elements  ds  and  ds'  of  the  circuits  be  called  r, 
and  e  the  angle  between  the  elements,  it  can  be  shown  that  their 

mutual  potential  is  =  —  ii'  j  I  —  —  ds  ds'.     This  expression  represents 

the  work  that  would  have  to  be  done  to  bring  up  either  of  the  circuits 
from  an  infinite  distance  to  its  present  position  near  the  other,  and 
is  a  negative  quantity  if  they  attract  one  another.  Now,  suppose 
the  strength  of  current  in  each  circuit  to  be  unity;  their  mutual 

potential  will  in  that  case  be  \  \  —  —  ds  ds',  a  quantity  which  depends 

purely  upon  the  geometrical  form  and  position  of  the  circuits,  and 
for  which  we  may  substitute  the  single  symbol  M,  which  we  will  call 
the  "  coefficient  of  mutual  potential  "  :  we  may  now  write  the  mutual 
potential  of  the  two  circuits  when  the  currents  are  i  and  i'  as 
=  -  it'M. 

But  we  have  seen  in  the  case  of  a  single  loop  circuit  that  we  may 
represent  the  potential  between  a  circuit  and  a  unit-pole  as  the 
product  of  the  strength  of  the  current  —  i  into  the  number  F  of  the 
magnet-pole's  lines  of  force  intercepted  by  the  circuit.  Hence 
the  symbol  M  must  represent  the  number  of  each  other's  lines  of 
force  mutually  intercepted  by  both  circuits,  if  each  carried  unit 
current,  and  if  each  consisted  of  one  turn  only.  If  the  circuits 
have  more  than  one  turn  each,  then  we  must  think  of  the  linkages 
which  each  circuit  makes  with  the  lines  of  the  other  circuit ;  and 
for  each  circuit  the  linkage  it  makes  will  be  equal  to  the  product 
of  the  number  of  its  turns  into  the  actual  number  of  lines  that  pass 
through  those  turns.  If  we  call  the  two  circuits  A  and  B,  then, 
when  each  carries  unit  current,  A  makes  M  linkages  with  the  lines 
of  force  belonging  to  B,  and  B  makes  M  linkages  with  the  lines  of 
force  belonging  to  A. 

Now  suppose  both  currents  to  run  in   the  same   (clock-wise) 


340  ELECTRICITY   AND   MAGNETISM     [PT.  n.  379 

direction;  the  front  or  S-seeking  face  of  one  circuit  will  be  oppo- 
site to  the  back  or  N-seeking  face  of  the  other  circuit,  and  they 
will  attract  one  another,  and  will  actually  do  work  as  they  approach 
one  another,  or  (as  the  negative  sign  shows)  negative  work  will  be 
done  in  bringing  up  one  to  the  other.  When  they  have  attracted 
one  another  up  as  much  as  possible  the  circuits  will  coincide  in 
direction  and  position  as  nearly  as  can  ever  be.  Their  potential 
energy  will  have  run  down  to  its  lowest  minimum,  their  mutual 
potential  being  a  negative  maximum,  and  their  coefficient  of  mutual 
potential  M  having  its  greatest  possible  value.  Two  circuits, 
then,  are  urged  so  that  their  coefficient  of  mutual  potential  M  shall 
have  the  greatest  possible  value.  This  justifies  Maxwell's  Rule  (Art. 
217),  because  M  represents  the  number  of  mutual  interlinkages  of 
either  circuit  with  the  lines  created  by  unit  current  in  the  other 
circuit.  And  since,  when  unit  current  is  turned  on  or  off  in  either 
circuit,  the  induced  electromotive-force  in  the  other  is  propor- 
tional to  their  mutual  interlinkage,  the  coefficient  M  is  also  called 
the  coefficient  of  mutual  inductance  (Art.  497,  p.  474). 

LESSON  XXVII.  —  The  Electromagnetic  System  of  Units 

379.  Magnetic  Units.  —  All  magnetic  quantities,  strength  of 
poles,  intensity  of  magnetization,  etc.,  are  expressed  in  terms  of 
special  units  derived  from  the  fundamental  units  of  length,  mass, 
and  time,  explained  in  the  Note  on  Fundamental  and  Derived  Units 
(Art.  298).  Most  of  the  following  units  have  been  directly  ex- 
plained in  the  preceding  Lesson,  or  in  Lesson  XI. ;  the  others 
follow  from  them. 

Unit  Magnet-pole.  —  The  unit  magnetic  pole  is  one  of  such 
a  strength,  that  when  placed  at  a  distance  of  1  centimetre 
(in  air)  from  a  similar  pole  of  equal  strength,  repels  it 
with  a  force  of  1  dyne  (Arts.  142  and  299). 

Magnetic  Potential.  —  Magnetic  potential  being  measured  by 
work  done  in  moving  a  unit  magnetic  pole  against  the 
magnetic  forces,  the  unit  of  magnetic  potential  will  be 
measured  by  the  unit  of  work  done  on  unit-pole. 

Unit  Difference  of  Magnetic  Potential.  —  Unit  difference  of 
magnetic  potential  exists  between  two  points  when  it 
requires  the  expenditure  of  one  erg  of  work  to  bring  a 
(N-seeking)  unit  magnetic  pole  from  one  point  to  the 
other  against  the  magnetic  forces. 

Intensity  of  Magnetic  Field  is  measured  by  the  force  it  exerts 
upon  a  unit  magnetic  pole  :  hence, 


CH.  v.  380]  ELECTROMAGNETIC   UNITS  341 

Unit  Intensity  of  Field  is  that  intensity  of  field  which  acts 
on  a  unit  (N-seeking)  pole  with  a  force  of  1  dyne.  The 
name  of  gauss  has  been  assigned  to  this  unit.  A  field 
having  an  intensity  of  6000  dynes  per  unit  pole  would  be 
described  as  6  kilogausses. 

Magnetic  Flux,  or  total  number  of  magnetic  lines.  Its  unit 
will  be  one  magnetic  line,  also  called  one  maxwell. 

Magnetomotive-Force,  or  line-integral  of  the  magnetizing  forces, 
is  proportional  to  the  current  and  to  the  number  of  turns 
in  the  magnetizing  coil  (see  Art.  368). 

Magnetic  Reluctance  (see  Art.  404)  is  the  ratio  of  magneto- 
motive-force to  magnetic  flux.  Unit  reluctance  will  be 
such  that  unit  magnetomotive-force  applied  to  it  generates 
in  it  a  flux  of  one  line. 

380.  Electromagnetic  Units.  —  The  preceding  magnetic  units 
give  rise  to  the  following  set  of  electrical  units,  in  which  the  strength 
of  currents,  etc.,  are  expressed  in  magnetic  measure.  They  are 
sometimes  called  "  absolute  C.G.S."  units.  The  relation  of  this 
"  electromagnetic  "  set  of  units  to  the  "  electrostatic  "  set  of  units 
of  Art.  301  is  explained  in  Art.  386. 

Unit  Strength  of  Current.  —  A  current  has  unit  strength  when 
one  centimetre  length  of  its  circuit  bent  into  an  arc  of 
one  centimetre  radius  (so  as  to  be  always  one  centimetre 
away  from  the  magnet-pole)  exerts  a  force  of  one  dyne 
on  a  unit  magnet-pole  placed  at  the  centre  (Art.  220). 

Unit  of  Difference  of  Potential  (or  of  Electromotive-force).  — 
Potential  is  work  done  on  a  unit  of  electricity ;  hence 
unit  difference  of  potential  exists  between  two  points 
when  it  requires  the  expenditure  of  one  erg  of  work  to 
bring  a  unit  of  +  electricity  from  one  point  to  the  other 
against  the  electric  force.  Also,  unit  electromotive-force 
is  generated  by  cutting  one  magnetic  line  per  second. 

Unit  of  Resistance.  —  A  conductor  possesses  unit  resistance 
when  unit  difference  of  potential  between  its  ends  causes 
a  current  of  unit  strength  to  flow  through  it. 

Unit  of  Quantity  of  Electricity  is  that  quantity  which  is  con- 
veyed by  unit  current  in  one  second. 

Unit  of  Capacity.  —  Unit  capacity  requires  unit  quantity  to 
charge  it  to  unit  potential. 

Unit  of  Induction.  —  Unit  induction  is  such  that  unit  electro- 
motive-force is  induced  by  the  variation  of  the  current  at 
the  rate  of  one  unit  of  current  per  second. 

>d  C         I  ^ 


342  ELECTRICITY   AND   MAGNETISM     [PT.  n.  331 

381.    Practical  Units   and    Standards.1  —  Several  of   the   above 

"  absolute  "  units  in  the   C.G.S.  system  would  be  inconveniently 

large    and    others    inconveniently    small    for    practical   use.     The 

following  are  therefore  chosen  as  practical  units :  — 

V    Resistance.  —  The    Ohm,  =  10°    absolute    units    of    resistance 

(and    theoretically    the    resistance    represented     by    the 

velocity  of  one  earth-quadrant  per  second,  see  Art.  384), 

but  actually  represented  by  the  resistance  of  a  uniform 

column  of  mercury   106'3  centimetres  long  and   14*4521 

grammes  in  mass,  at  0°  C.     Such  a  column  of  mercury  is 

represented  by  a  "  standard  "  ohm  (see  Art.  385). 

Current.  —  The  Ampere,  =  10 -1  absolute  units;  practically 
represented  by  the  current  which  deposits  silver  at  the 
rate  of  O'OOlllS  gramme  per  second  (see  Appendix  B). 
^,  Electromotive-force.  —  The  Volt,  =  10*  absolute  units,  is  that 
E.M.F.  which  applied  to  1  ohm  will  produce  in  it  a  current 
of  1  ampere  ;  being  j£||  of  the  E.M.F.  of  a  Clark  standard 
cell  at  14°  C. 

Quantity.  —  The  Coulomb,  =  10-1  absolute  units  of  quantity; 
being  the  quantity  of  electricity  conveyed  by  1  ampere 
in  one  second. 

Capacity.  —  The  Farad,  =  10"9  (or  one  one-thousand-millionth) 
of  absolute  unit  of  capacity ;  being  the  capacity  of  a 
condenser  such  as  to  be  changed  to  a  potential  of  1  volt 
by  1  coulomb.  The  microfarad  or  millionth  part  of  1 
farad  =  10  ~15  absolute  units. 

Work.  —  The  Joule,  =  107  absolute  units  of  work  (ergs),  is  repre- 
sented by  energy  expended  per  second  by  1  ampere  in  1  ohm. 

Power.  —  The  Watt,  =  107  absolute  units  of  power  (ergs  per 
second),  is  power  of  a  current  of  1  ampere  flowing  under 
a  pressure  of  1  volt.  It  is  equal  to  1  joule  per  second, 
and  is  approximately  7£T  of  one  horse-power. 

Inductance.  —  The  Henry,  =  109  absolute  units  of  inductance, 
is  the  inductance  in  a  circuit  when,  while  the  inducing 
current  varies  at  the  rate  of  1  ampere  per  second,  the 
electromotive-force  induced  in  this  circuit  is  1  volt. 

Conductance.  —  The  Siemens,  =  10~9  absolute  units  of  con- 
ductance, and  is  the  reciprocal  of  the  ohm.  (Formerly 
called  the  "  mho.") 

1  The  word  "unit"  expresses  our  conception  in  tne  abstract  of  a  unit 
quantity,  such  as  those  denned  in  the  preceding  Articles.  A  "standard" 
is  the  concrete  thing  with  which  we  compare  quantities  to  be  measured, 
such  as  a  centimetre  scale  or  a  standard  cell. 


.CH.  v.  382, 383]      DIMENSIONS    OF    UNITS  343 

Seeing,  however,  that  quantities  a  million  times  as  great  as 
some  of  these,  and  a  million  times  as  small  as  some,  have  to  be 
measured  by  electricians,  the  prefixes  mega-  and  micro-  are  some- 
times used  to  signify  respectively  "  one  million  "  and  "  one-millionth 
part."  Thus  a  megohm  is  a  resistance  of  one  million  ohms,  a 

microfarad  a  capacity  of     ^^         of  a  farad,  etc.     The  prefix  kilo- 
1 ,000,000 

is  used  for  "  one  thousand,"  and  milli-  for  "  one- thousandth  part  "  ; 
thus  a  kilowatt  is  1000  watts,  and  milliampere  is  the  thousandth 
part  of  1  ampere. 

The  "  practical  "  system  may  be  regarded  as  a  system  of  units 
derived  not  from  |he  fundamental  units  of  centimetre,  gramme,  and 
second,  but  from  a  system  in  which,  while  the  unit  of  time  remains 
the  second,  the  units  of  length  and  mass  are  respectively  the  earth- 
quadrant  and  10~ u  gramme. 

382.  Use  of  Index  Notation.  —  Seeing  that  electricians  have  to 
deal  with  quantities  requiring  in  some  cases  very  large  numbers, 
and  in  other  cases  very  small  numbers,  to  express  them,  a  system 
of  index  notation  is  adopted,  in  order  to  obviate  the  use  of  long 
rows  of  ciphers.     In  this  sytem  the  significant  figures  only  of  a 
quantity  are  put  down,  the  ciphers  at  the  end,  or  (in  the  case  of  a 
long  decimal)  at  the  beginning,  being  indicated  by  an  index  written 
above.     Accordingly,  we  may  write  a  thousand  ( =  10  x  10  X  10) 
as  103,  and  the  quantity  42,000  may  be  written    42  X  103.     The 
British  National  Debt  of  £  720,000,000  may  be  written  £  72  X  107. 
Fractional  quantities  will  have  negative  indices  when  written  as 
exponents.     Thus  T^  (=  O'Ol)  =  1  -5-  10  -5-  10  =  10~2.     And  so  the 
decimal  0*00028  will  be  written  28  X  105  (being  =  28  X  O'OOOOl). 
The  convenience  of  this  method  will  be  seen  by  an  example  or  two 
on  electricity.     The  electrostatic  capacity  of  the  earth  is  630,000,000 
times  that  of  a  sphere  of  one  centimetre  radius,  =  63  X  107  (elec- 
trostatic) units.     The  resistance  of  selenium  is  about  40,000,000,000, 
or  4  X  1010  times  as  great  as  that  of  copper;    that  of  air  is  about 
1026,  or 

100,000,000,000,000,000,000,000,000 

times  as  great.  The  velocity  of  light  is  about  30,000,000,000 
centimetres  per  second,  or  3  X  1010. 

383.  Dimensions   of   Magnetic   and   Electromagnetic   Units.  — 
The  fundamental  idea  of  "  dimensions  "  is  explained  in  Art.  302. 
A  little  consideration  will  enable  the  student  to  deduce  for  himself 
the  following  table,  wherein  the  symbol  M  relates  (see  Art.  390)  to 
the  magnetic  permeability  of  the  medium  :  — 


344 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  384 


UNITS 

DIMENSIONS 

(Magnetic) 

[ 

Strength  of  pole 

m 

Quantity  of  magnet- 

= \/force  X  (distance)2  X  M        = 

M^  L$  T—  V^ 

I 

ism                             J 

V 

Magnetic  Potential 

=  work  -7-  strength  of  pole 

M}L*T-IM-* 

Intensity  of  Field 

=  force  -T-  strength  of  pole 

M*  L^T"1""' 

. 

Magnetic  Flux 

=  intensity  X  area                           = 

M*  L?  T-i^i* 

z 

Reluctance 

=  mag.  potential  -f-  flux 

L-i  ^1 

(Electromagnetic) 

i 

Current  (strength) 

=  intensity  of  field  X  length        = 

M^L^T"1  M~l 

Q 

Quantity  (charge) 

—  current  X  time                             = 

Ma  LI  M-* 

V 

Potential                      \ 

^ 

E 

Electromotive-force    j 

=  work  -f-  quantity      .                   = 

M^L^T"2  p.* 

R 

Resistance 

=  E.M.F.  -7-  current 

jjrj,_lj0tl 

C 

Capacity 

quantity  -f-  potential             = 

L-iT*  M-i 

W 

Power 

=  current  X  potential 

ML2T-3 

L 

Self-Inductance           1 

M 

Mutual  Inductance    J 

=  E.M.F.  -T-  current  per  sec.       = 

L1"1 

X 

Electric-force 

=  force  -f-  quantity             1 

1    i           i 

Y 

Potential  gradient 

=  potential  -5-  length          J 

M2L2T"2M2 

For  electrostatic  units,  see  Art.  302,  p.  279. 

384.  Resistance  expressed  as  a  Velocity.  —  It  will  be  seen, 
on  reference  to  the  above  table  of  "  Dimensions  "  of  electromagnetic 
units,  that  the  dimensions  of  resistance  are  given  as  LT-1,  which 
are  the  same  dimensions  (see  Art.  302)  as  those  of  a  velocity.  Every 
resistance  is  capable  of  being  expressed  as  a  velocity.  The  following 
considerations  may  assist  the  student  in  forming  a  physical  con- 
ception of  this.  Suppose  we  have  a  circuit  composed  of  two  hori- 
zontal rails  (Fig.  197),  CS  and  DT,  1  centim.  apart,  joined  at  CD, 
and  completed  by  means  of  a  sliding  piece  AB.  Let  this  variable 

circuit  be  placed  in  a  uniform 
magnetic  field  of  unit  intensity, 
the  lines  of  force  being  directed 
vertically  downwards  through 
the  circuit.  If,  now,  the  slider 
be  moved  along  towards  ST 
with  a  velocity  of  n  centimetres 
per  second,  the  number  of  ad- 
ditional lines  of  force  embraced  by  the  circuit  will  increase  at  the  rate 
n  per  second ;  or,  in  other  words,  there  will  be  an  induced  electro- 
motive-force (Art.  243)  impressed  upon  the  circuit,  which  will  cause 
a  current  to  flow  through  the  slider  from  A  to  B.  Let  the  rails  have 
no  resistance,  then  the  strength"  of  the  current  will  depend  on  the 
resistance  of  AB.  Now  let  AB  move  at  such  a  rate  that  the  current 


FIG.   197.  —  Slider  cutting  the  Magnetic 
Lines  of  a  Field. 


CH.  v.  385] 


EVALUATION   OF   THE    OHM 


345 


shall  be  of  unit  strength.  If  its  resistance  be  one  "  absolute  " 
(electromagnetic)  unit  it  need  only  move  at  the  rate  of  1  centini. 
per  second.  If  its  resistance  be  greater  it  must  move  with  a  pro- 
portionately greater  velocity ;  the  velocity  at  which  it  must  move 
to  keep  up  a  current  of  unit  strength  [being  numerically  equal  to  its 
resistance.  The  resistance  known  as  "  one  ohm  "  is  intended  to  be 
109  absolute  electromagnetic  units,  and  therefore  is  represented  by  a 
velocity  of  109  centimetres,  or  ten  million  metres  (one  earth-quadrant) 
per  second. 

385.  Evaluation  of  the  Ohm.  —  The  system  of  "  practical  " 
units  was  originally  devised  by  a  committee  of  the  British  Associa- 
tion, who  also  determined  the  value  of  the  "  ohm  "  by  experiment 
in  1863,  and  constructed  standard  resistance  coils  of  German-silver, 
called  "  B.A.  Units  "  or  "  ohms." 

There  are  several  ways  of  measuring  the  absolute  value  of  the 
resistance  of  a  wire.  One  method  (Joule's)  is  to  measure  the  heat 
produced  in  it  by  a  known  current  and  calculate  its  resistance  by 
Joule's  law  (Art.  462).  Another  method  (Weber's)  is  to  measure 
in  absolute  units  the  current  that  is  sent  through  the  wire  by  an 
electromotive-force  which  is  also  measured  in  some  absolute  way. 
The  ratio  of  the  latter  to  the  former 
gives  the  value  of  the  resistance. 
Weber's  method  involved  spinning  a 
coil  in  a  magnetic  field  which  would 
generate  alternating  currents.  Kohl- 
rausch  used  an  induction  coil  to  gen- 
erate the  E.M.F.  Lorenz  proposed 
a  method  in  which  a  disk  was  spun  in 
a  very  uniform  magnetic  field.  Foster 
used  a  zero  method  in  which  the 
E.M.F.  in  the  spinning  coil  was  bal- 
anced. Lord  Kelvin  proposed  to 
the  British  Association  Committee  a 
modification  of  Weber's  method  as  follows.  It  being  impracticable 
to  give  to  a  horizontal  sliding-piece  so  high  a  velocity  as  was  neces- 
sitated, the  velocity  which  corresponded  to  the  resistance  of  a  wire 
was  measured  in  the  following  way  :  —  A  ring  of  wire  (of  many  turns), 
pivoted  about  a  vertical  axis,  as  in  Fig.  198,  was  made  to  rotate 
very  rapidly  and  uniformly.  Such  a  ring  in  rotating  cuts  the  lines 
of  force  of  the  earth's  magnetism.  The  northern  half  of  the  ring,  in 
moving  from  west  toward  east,  will  have  (see  Rule,  Art.  243)  an  up- 
ward current  induced  in  it,  while  the  southern  half,  in  crossing  from 
east  toward  west,  will  have  a  downward  current  induced  in  it.  Hence, 


FIG.   198.  —  Kelvin's  Method  of  de- 
termining Value  of  Resistance. 


346 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  385 


FIG.   199.  —  Standard  One-Ohm  Coil. 


the  rotating  ring  will,  as  it  spins,  act  as  its  own  galvanometer  if  a  small 
magnet  be  hung  at  its  middle ;  the  magnetic  effect  due  to  the  rotat- 
ing coil  being  proportional  directly  to  the  horizontal  component 
of  the  earth's  magnetism,  to  the  velocity  of  rotation,  and  to  the 
number  of  turns  of  wire  in  the  coil,  and  inversely  proportional  to 
the  resistance  of  the  wire  of  the  coils.  Hence,  all  the  other  data 
being  known,  the  resistance  can  be  calculated  and  measured  as  a 

velocity.  The  earliest  ohms  or 
B.A.  units  were  constructed  by 
comparison  with  this  rotating 
coil ;  but  there  being  some  doubt 
as  to  whether  the  B.A.  unit  really 
represented  109  centims.  per  sec- 
ond, a  redetermination  of  the 
ohm  was  suggested  in  1880  by  the 
British  Association  Committee. 
At  the  first  International  Con- 
gress of  Electricians  in  Paris  1881, 
the  project  for  a  redetermination 
of  the  ohm  was  endorsed,  and  it 
was  also  agreed  that  the  practical 
standards  should  no  longer  be 
constructed  in  German-silver  wire,  but  that  they  should  be  made 
upon  the  plan  originally  suggested  by  Siemens,  by  denning  the 
practical  ohm  as  the  resistance  of  a  column  of  pure  mercury  of  a 
certain  length,  and  of  one  millimetre  of  cross-section.  The  original 
"  Siemens'  unit  "  was  a  column  of  mercury  one  metre  in  length, 
and  one  square  millimetre  in  section,  and  was  rather  less  than  an 
ohm  (0-9540  B.A.  unit).  Acting  on  measurements  made  by  lead- 
ing physicists  of  Europe,  the  Paris,  Congress  of  1884  decided  that 
the  mercury  column  representing  the  "  legal  "  ohm  should  be  106 
centimetres  in  length.  This  was,  however,  never  legalized  in  this 
country  or  in  America,  as  it  was  known  to  be  incorrect.  Lord 
Rayleigh's  determination  gave  106*21  centimetres  of  mercury,  as 
representing  the  true  theoretical  ohm  ( =  109  absolute  units) ;  and 
Rowland's  determinations  at  Baltimore  came  slightly  higher. 
The  British  Association  Committee  in  1892  agreed  to  lengthen  it  to 
106.3  centims.,  and  to  define  by  mass  instead  of  section.  This 
was  decided  as  the  international  ohm  by  the  Congress  of  Chicago 
in  1893  and  reaffirmed  by  the  International  Conference  in  London 
in  1908.  These  international  units  are  now  legalized  in  England 
and  the  United  States.  The  order  approved  by  His  Majesty  in 
Council  and  issued  through  the  Board  of  Trade  is  given  in  Appen- 


CH.  v.  386] 


RATIO   OF   UNITS 


347 


dix  B.  Recently  F.  E.  Smith,  of  the  National  Physical  Laboratory, 
using  Lorenz's  method  perfected  by  Viriamu  Jones  and  Ayrton, 
has  found  the  exact  value  of  the  ohm,  in  terms  of  the  length  of 
mercury  column  to  be  106*245  cms.  The  old  B.A.  unit  is  only 
0.9863  of  the  true  ohm;  the  Siemens'  unit  is  only  0'9408.  Fig. 
199  depicts  a  standard  one-ohm  coil  as  sold  commercially1.  It 
consists  of  a  resistance  coil  (Art.  446)  of  suitable  wire  adjusted 
to  be  exactly  equal  to  the  primary  standard  ohm  that  is  legal  in 
this  country. 

386.  Ratio  of  the  Electrostatic  to  the  Electromagnetic  Units.  — 
If  the  student  will  compare  the  Table  of  Dimensions  of  Electrostatic 
Units  of  Art.  302  with  that  of  the  Dimensions  of  Electromagnetic 
Units  of  Art.  383,  he  will  observe  that  the  dimensions  (in  length, 
mass,  and  time)  assigned  to  similar  units  are  different  in  the  two 
systems.  Thus,  the  dimensions  of  "  Quantity "  in  electrostatic 

measure  are  M^  L/2  T-1,  and  in  electromagnetic  measure  they  are 

M1  IA  Dividing  the  former  by  the  latter  we  get  LT-1,  a  quantity 
which  we  at  once  see  is  of  the  nature  of  a  velocity.  This  velocity, 
occurs  in  every  case  in  the  ratio  of  the  electrostatic  to  the  elec- 
tromagnetic measure  of  every  unit.  It  is  a  definite  concrete  velocity 
and  represents  that  velocity  at  which  two  electrified  particles  must 
travel  along  side  by  side  in  order  that  their  mutual  electromagnetic 
attraction  (considered  as  equivalent  in  so  moving  (Art.  429)  to  two 
parallel  currents)  shall  just  equal  their  mutual  electrostatic  re- 
pulsion (see  Art.  277).  This  velocity,  "  v,"  which  is  of  enormous 
importance  in  the  electromagnetic  theory  of  light  (Art.  609),  has  been 
measured  in  several  ways. 


UNIT 

..  ELECTROSTATIC 

ELECTROMAGNETIC 

RATIO 

Quantity 
Potential 
Capacity 
Resistance 

WUT-W 
MJLiT-i  fc-i 

L          A;1 
L-1T    AT1 

M*  L*        /*-* 
M*Li  T~2  & 
L-*T2  AT* 
L    T"1/*1 

LT'1  jfe»  IJ    =v 
L^TAT*  A*-*  =l/v 

L-2T-2£i      Ml       =  0-2 

L-2T2Ar!  A*'1  =  l/vz 

(a)  Weber  and  Kohlrausch  measured  the  electrostatic  unit  of 
quantity  and  compared  it  with  the  electromagnetic  unit  of  quantity, 
and  found  the  ratio  v  to  be  =  3' 1074  X  1010  centims.  per  second. 

(fe)  Lord  Kelvin  compared  the  two  units  of  potential  and  found 

v          =  2-825     X  1010, 
and  later,         =  2'93       X  1010. 


348          ELECTRICITY  AND   MAGNETISM    [PT.  n.  387,  388 

(c)  Professor  Clerk  Maxwell  balanced  a  force  of    electrostatic 
attraction  against  one  of  electromagnetic  repulsion,  and  found 

v        =  2-88       X  1010. 

(d)  Professors  Ayrton  and   Perry  measured   the   capacity  of  a 
condenser  electromagnetically  by   discharging  it  into   a  ballistic 
galvanometer,  and  electrostatically  by  calculations  from  its  size, 
and  found 

v        =  2-980     X  1010. 

The  mean  value,  according  to  the  most  recent  researches  is :  — 

v        =2-999      X  1010. 

The  velocity  of  light  according  to  latest  values  is  — 
=  2-9986   X  1010; 

so  we  take  v  as  3  X  1010,  or  thirty  thousand  million  centimetres  per 
second. 

387.  Rationalization     of     Dimensions     of     Units.  —  It     seems 
absurd  that  there  should  be  two  different  units  of  electricity ;   still 
more  absurd  that  one  unit  should  be  thirty  thousand  million  centi- 
metres per  second  greater  than  the  other.     It  also  seems  absurd 
that  the  dimensions  of  a  unit  of  electricity  should  have  fractional 

powers,  since  such  quantities  as  M1  and  L^  are  meaningless.  These 
irrational  things  arise  from  the  neglect  to  take  account  of  the 
properties  of  the  medium  in  applying  the  law  of  inverse  squares 
to  form  definitions  of  the  unit  of  electricity  in  the  electrostatic 
system,  and  of  the  unit-pole  in  the  magnetic  system.  If  we  insert 
(Art.  302)  the  inductivity  k  in  the  former,  and  the  permeability 
H  in  the  latter,  we  might,  if  we  knew  the  dimensions  of  these  quanti- 
ties, be  able  to  rationalize  the  dimensional  formulae.  But  we  do 
not  know  their  dimensions.  Riicker  has,  however,  shown  that 
they  can  be  rationalized,  and  the  two  sets  of  units  brought  into 
agreement,1  by  assuming  that  the  product  kp  has  the  dimensions 
of  the  reciprocal  of  the  square  of  a  velocity:  or  v  =  1/V/c/x.  If 
k  were  the  reciprocal  of  the  rigidity  of  the  ether,  and  p  its  density, 
v  would  represent  the  velocity  of  propagation  of  waves  in  it. 
Compare  Art.  609  on  the  electromagnetic  theory  of  light. 

388.  Earth's  Magnetic  Force  in  Absolute  Units.  —  In  making 
absolute  determinations  of  current  by  the  tangent  galvanometer, 
or  of  electromotive-force  by  the  spinning  coil,  it  is  needful  to  know 
the  absolute  value  of  the  earth's  magnetic  field,  or  of  its  horizontal 

1  See  Everett's  Units  and  Physical  Constants,  4th  edition  (1893),  p.  208. 


CH.  v.  388]          MAGNETIC   MEASUREMENTS  349 

component.  The  intensity  of  the  earth's  magnetic  force  at  any 
place  is  the  force  with  which  a  magnet-pole  of  unit  strength  is 
attracted.  As  explained  in  Art.  159,  it  is  usual  to  measure  the 
horizontal  component  H  of  this  force,  and  from  this  and  the  cosine 
of  the  angle  of  dip  to  calculate  the  total  force,  as  the  direct  deter- 
mination of  the  latter  is  surrounded  with  difficulties.  To  deter- 
mine H  in  absolute  (or  C.G.S.)  units,  it  is  necessary  to  make  two 
observations  with  a  magnet  of  magnetic  moment  M  (Art.  137). 
In  one  of  these  observations  the  product  MH  is  determined  by  a 
method  of  oscillations  (Art.  135) ;  in  the  second  the  quotient  M/H  is 
determined  by  a  particular  method  of  deflexion  (Art.  140).  The 
square  root  of  the  quantity  obtained  by  dividing  the  former  by  the 
latter  will,  of  course,  give  H. 

(i)   Determination  of  MH.  —  The  time  T  of  a  complete  oscilla- 
tion to  and  fro  of  a  magnetic  bar  is 


where  K  is  the  "  moment  of  inertia  "  of  the  magnet,  and  n  is  the 
frequency  of  vibration.  This  formula  is,  however,  only  true  for 
very  small  arcs  of  vibration.  By  simple  algebra  it  follows  that 

MH  =  m^K  -r-  T2. 

Of  these  quantities  T  is  ascertained  by  a  direct  observation  of 
the  time  of  oscillation  of  the  magnet  hung  by  a  torsionless  fibre; 
and  K  can  be  either  determined  experimentally  or  by  one  of  the 
following  formulae :  — 

For  a  round  bar  K  =  w(~  +  —  V 


For  a  rectangular  bar         K  =  wl  — — ^  j  ; 


where  w  is  the  mass  of  the  bar  in  grammes,  I  its  length,  a  its  radius 
(if  round),  b  its  breadth,  measured  horizontally  (if  rectangular). 

(ii)  Determination  of  M/H.  —  The  magnet  is  next  caused  to  de- 
flect a  small  magnetic  needle  in  the  following  manner,  "  broadside 
on."  The  magnet  is  laid  horizontally  at  right  angles  to  the  mag- 
netic meridian,  and  so  that  its  middle  point  is  (magnetically)  due 
south  or  due  north  of  the  small  needle,  and  at  a  distance  r  from  its 
centre.  Lying  thus  broadside  to  the  small  needle  its  N-pole  will 
repel,  and  its  S-pole  attract,  the  N-pole  of  the  needle,  and  will 
exercise  contrary  actions  on  the  S-pole  of  the  needle.  The  total 
action  of  the  magnet  upon  the  needle  will  be  to  deflect  the  latter 


350          ELECTRICITY  AND   MAGNETISM    [PT.  n.  389,  390 

through  an  angle  5,  whose  tangent  is  directly  proportional  to  M/H, 
and  inversely  proportional  to  the  cube  of  the  distance  r ;  or 

M/H  =  r3  tan  5. 

Dividing  the  former  equation  by  this,  and  taking  the  square  root, 
we  get 

H 


T    VtanS 

LESSON  XXVIII.  —  Properties  of  Iron  and  Steel 

389.  Magnetization  of  Iron.  —  When  a  piece  of  magnetiz- 
able metal  is  placed  in  a  magnetic  field,  some  of  the  lines  of 
magnetic  force  run  through  it  and  magnetize  it.     The  in- 
tensity of  its  magnetization  will  depend  upon  the  intensity  of 
the  field  into  which  it  is  put  and  upon  the  metal  itself.     There 
are  two  ways  of  looking  at  the  matter,  each  of  which  has  its 
advantages.     We  may  think  about  the  internal  condition 
of  the  piece  of  metal,  and  of  the  number  of  magnetic  lines  that 
are  running  through  it  and  emerging  from  it  into  the  sur- 
rounding space.     This  is  the  modern  way.     Or  we  may  think 
of  the  magnetism  of  the  iron  or  other  metal  as  something  resi- 
dent on  the  polar  surfaces,  and  expressed  therefore  in  units 
of  magnetism.     This  is  the  old  way.     The  fact  that  soft  iron 
placed  in  the  magnetic  field  becomes  highly  magnetic  may 
then  be  expressed  in  the  following  two  ways  :    (1)  when  iron 
is  placed  in  the  magnetic  field,  the  magnetic  lines  run  in 
greater  quantities  through  the  space  now  occupied  by  iron, 
for  iron  is  very  permeable  to  the  lines  of  magnetic  induction, 
being  a  good  conductor  of  the  magnetic  lines ;     (2)  iron 
when  placed  in  the  magnetic  field  develops  strong  poles 
on  its  end-surfaces,  being  highly  susceptible  to  magnetiza- 
tion.    Each  of  these  ideas  may  be  rendered  exact  by  the 
introduction  of  appropriate  coefficients. 

390.  Permeability.  —  Suppose   a   magnetic   force  —  due, 
let  us  say,  to  the  circulation  of  an  electric  current  in  a  sur- 
rounding coil  —  were  to  act  on  a  space  occupied  by  air, 


CH.  v.  390]  PERMEABILITY  351 

there  would  result  a  certain  number  of  magnetic  lines 
in  that  space.  In  fact,  the  intensity  of  the  magnetic  force, 
symbolized  by  the  letter  §,  is  often  expressed  by  saying  that 
it  would  produce  §  magnetic  lines  per  square  centimeter 
in  air.  Now,  owing  to  the  superior  magnetic  properties  of 
iron,  if  the  space  subjected  to  this  magnetic  force  were  filled 
with  iron  instead  of  air,  there  would  be  produced  a  larger 
number  of  magnetic  lines  per  square  centimetre.  This 
larger  number  expresses  the  degree  of  magnetization  l  or 
density  of  the  magnetic  flux  in  the  iron  ;  it  is  symbolized  by 
the  letter  33.  The  ratio  of  33  to  §  expresses  the  permeabil- 
ity of  the  material.  The  usual  symbol  for  the  permeability 
is  the  Greek  letter  p.  So  we  may  say  that  the  flux-density 
33  is  equal  to  /*  times  the  magnetic  force  §,  or 


Example.  —  A  certain  specimen  of  iron,  when  subjected  to  a 
magnetic  force  capable  of  creating,  in  air,  50  magnetic 
lines  to  the  square  centimetre,  was  found  to  be  permeated 
by  no  fewer  than  16,062  magnetic  lines  per  square  centi- 
metre. Dividing  the  latter  figure  by  the  former  gives  as 
the  value  of  the  permeability  at  this  stage  of  the  mag- 
netization 321,  or  the  permeability  of  the  iron  is  321 
times  that  of  air. 

The  permeability  is  always  positive  :  for  empty  space  it 
is  1,  for  air  and  all  non-magnetic  substances  as  cotton,  silk, 
and  other  insulators,  and  for  copper,  brass,  and  the  non-mag- 
netic metals,  it  is  practically  1.  In  all  these  therefore  33  =$. 
For  magnetic  metals,  iron,  cobalt,  and  nickel,  the  permeabil- 
ity is  greater  than  1.  For  diamagnetic  materials  (Art.  399) 
it  is  slightly  less  than  1. 

Where  the  magnetic  lines  emerge  into  the  air  at  a  polar 

1  Flux-density,  the  number  of  magnetic  lines  that  run  through  unit  area 
of  cross-section  in  the  iron  or  other  material  —  also  denoted  by  the  symbol 
SB  —  is  called  by  several  names  —  "the  permeation,"  "the  internal  mag- 
netization," or  "the  induction."  The  last  name,  unfortunately  used  by 
Maxwell  and  Hopkinson,  is  to  be  avoided,  since  "induction"  was  intro- 
duced by  Faraday  to  denote  the  operation  of  inducing  electromotive  force. 


352  ELECTRICITY   AND   MAGNETISM     [PT.  n.  391 

surface  they  are  of  course  continuous  with  the  internal 
lines :  the  value  of  33  just  inside  the  polar  surface  is  the 
same  as  that  of  33  in  the  air  just  outside  it. 

This  mode  of  expressing  the  facts  is,  however,  complicated 
by  the  fact  of  the  tendency  to  magnetic  saturation  in  all 
kinds  of  iron.  In  all  kinds  of  iron  the  magnetizability  of 
the  material  becomes  diminished  as  the  actual  magnetiza- 
tion is  pushed  further.  In  other  words,  when  a  piece  of  iron 
has  been  magnetized  up  to  a  certain  degree,  it  becomes,  from 
that  degree  onward,  less  permeable  to  further  magnetization, 
and  though  actual  saturation  is  never  reached,  there  is  a 
practical  limit  beyond  which  it  cannot  well  be  pushed.  Joule 
discovered  this  tendency  to  a  limit.  The  practical  limit  of  33 
in  good  wrought  iron  is  about  20,000  lines  per  square  centi- 
metre, or  in  cast  iron  about  12,000.  Using  extraordinary 
magnetizing  forces,  Ewing  has  found  it  possible  to  increase 
33  to  45,000,  and  Du  Bois  has  reached  60,000  lines  per  square 
centimetre. 

391.    Curves  of  Magnetization.  —  A  convenient  mode  of 
studying  the  magnetic  facts  respecting  any  particular  brand 
of  iron  is  to-  plot  on  a  diagram  the  curve  of  magnetization  — 
i.e.  the  curve  in  which  the  values, 
plotted  horizontally,   represent   the 
magnetic   force  §,   and  the  values 
plotted  vertically  those  that  corre- 
spond to  the  respective  magnetiza- 
tion 33.     In  Fig.  200,  which  is  modi- 
fied from  the  researches  of  Ewing, 
FIG.  200.  —  Ewing-a  Curves  of    are  given  five  curves  relating  to  soft 
iron,  hardened  iron,  annealed  steel, 

hard-drawn  steel,  and  glass-hard  steel.  It  will  be  noticed 
that  all  these  curves  have  the  same  general  form,  and  that 
there  are  three  stages.  (1)  For  small  values  of  §  the  values 
of  33  are  small,  and  as  §  is  increased  33  increases  gradually. 
(2)  The  curve  rises  very  suddenly,  at  least  with  all  the  softer 
sorts  of  iron.  (3)  The  curve  then  bends  over  and  becomes 


CH.  v.  391]        CURVES   OF   MAGNETIZATION 


353 


nearly  horizontal,  $8  increasing  very  slowly.  The  three 
stages  observed  in  the  magnetization  are  explained  in  Swing's 
molecular  theory  (Art.  129).  When  the  magnetization  is  in 
the  stage  below  the  bend  of  the  curve,  the  iron  is  said  to  be 
far  from  the  state  of  saturation.  But  when  the  magnetiza- 
tion has  been  pushed  beyond  the  bend  of  the  curve  into  the 
third  stage,  the  iron  is  said  to  be  approaching  saturation,  be- 
cause at  this  stage  of  magnetization  it  requires  a  large  in- 
crease in  the  magnetizing  force  to  produce  even  a  very  small 
increase  in  the  magnetization.  It  will  be  noted  that  for  soft 
wrought  iron  the  stage  of  approaching  saturation  sets  in 
when  33  has  attained  the  value  of  about  16,000,  or  when  § 
has  been  raised  to  about  50.  The  student  is  strongly  advised 
to  plot  for  himself  similar  curves  from  the  subjoined  table, 
which  relates  to  the  permeabilities  of  some  samples  of  iron 
examined  by  Hopkinson. 


ANNEALED  WROUGHT  IRON 

GREY  CAST  IRON 

$ 

23 

/* 

% 

33 

/* 

1'66 

5,000 

3000 

5 

4,000 

800 

4 

9,000 

2250 

10 

5,000 

500 

5 

10,000 

2000 

21'5 

6,000 

279 

6'5 

11,000 

1692 

42 

7,000 

133 

8'5 

12,000 

1412 

80 

8,000 

100 

12 

13,000 

1083 

127 

9,000 

71 

17 

14,000 

823 

188 

10,000 

53 

28'5 

15,000 

526 

292 

11,000 

37 

50 

16,000 

320 

105 

17,000 

161 

200 

18,000 

90 

350 

19,000 

54 

666 

20,000 

30 

At  early  stages  of  the  magnetization,  in  moderately  weak 
fields  where  @  is  less  than  about  5,  the  permeability  reaches 
3000  or  4000.  But  for  values  of  §  less  than  about  0-04  the 
permeability  of  iron  is  quite  small,  usually  from  100  to  120. 

2A 


354 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  391 


Iron  reheated  in  vacuo  may  reach  a  permeability  of  10,000 
or  12,000. 

An  alloy  of  iron  with  3 '4  per  cent  of  silicon,  known  as 
stalloy,  invented  by  Hadfield,  has  a  permeability  nearly  as 


high  as  wrought  iron,  and  has  low  hysteresis  with  high  elec- 
trical resistance,  being  therefore  excellent  for  laminated  cores. 
In  Fig.  201,  and  in  the  Table  on  p.  355,  some  additional 
data  are  given  ;  but  here  the  values  of  the  magnetizing  force 


CH.  v.  392] 


SUSCEPTIBILITY 


355 


are  stated  not  in  terms  of  the  intensity  of  field,  §,  but  in 
terms  of  the  magnetizing  ampere-turns  per  centimetre  length 
of  the  substance ;  this  being  more  convenient  for  the  calcu- 
lations. 


MAGNETIZING 
FORCE,  EX- 
PRESSED IN 
AMPERE- 
TURNS  PER 
CENTIMETRE 

VALUES  OF  FLUX-DENSITY,  $Q,  IN  LINES  PER  SQUARE  CENTIMETRE 

Lohyg  Sheet 
Iron 
(Sankey) 

Soft  Mag- 
net Steel 
(HadGeld) 

Wrought 
Iron 
(Hopkinson) 

Cast  Mild 
Steel 
(E.  Allen) 

Grey  Cast 
Iron 
(Hopkinson) 

0-5 

2,600 

200 

200 

350 

180 

it) 

4,600 

300 

300 

800 

250 

2*0 

•      7,200 

1,400 

900 

3,000 

550 

3'0 

9,700 

6,000 

4,000 

6,000 

900 

4'0 

11,200 

8,600 

7,100 

8,200 

1,300 

5'0 

12,400 

10,200 

8,800 

9,600 

1,800 

6'0 

13,100 

11,400 

9,850 

10,600 

2,500 

7'0 

13,800 

12,400 

10,700 

11,400 

3,300 

8'0 

14,100 

13,100 

11,400 

12,200 

3,900 

9'0 

14,700 

13,700 

11,950 

12,800 

4,400 

20 

15,000 

14,300 

12,500 

13,300 

4,700 

12'5 

15,600 

15,150 

13,300 

14,200 

5,300 

15 

16,000 

15,800 

13,850 

14,900 

5,600 

17'5 

16,250 

16,050 

14,200 

15,400 

5,850 

20 

16,350 

16,500 

14,500 

15,750 

6,000 

30 

16,750 

17.000 

15,300 

16,800 

6,550 

40 

17,150 

17,300 

15,700 

17,150 

7,000 

50 

17,500 

17,600 

16,000 

17,550 

7,400 

60 

17,700 

17,900 

16,200 

17,900 

7,800 

If  iron  is  compressed  its  permeability  decreases;  if  sub- 
jected to  tensile  stress  it  is  increased,  provided  the  field  is  not 
too  intense.  Villari  found  that  beyond  a  certain  intensity 
tension  diminishes  the  permeability. 

392.  Susceptibility.  —  Suppose  a  magnet  to  have  m  units 
of  magnetism  on  each  pole ;  then  if  the  length  between  its 
poles  is  I,  the  product  ml  is  called  its  magnetic  moment,  and  the 
magnetic  moment  divided  by  its  volume  is  called  its  intensity 
of  magnetization;  this  term  being  intended,  though  based  on 
surface-unit  of  pole  strength,  to  convey  an  idea  as  to  the 
internal  magnetic  state.  Seeing  that  volume  is  the  product 


356  ELECTRICITY   AND   MAGNETISM      [PT.  n.  392 

of  sectional  area  into  length,  it  follows  that  if  any  piece  of  iron 
or  steel  of  uniform  section  had  its  surface  magnetism  situated 
on  its  ends  only,  its  intensity  of  magnetization  would  be  equal 
to  the  strength  of  pole  divided  by  the  area  of  end  surface. 
Writing  £  for  the  intensity  of  magnetization  we  should  have 
<£  _  mag,  moment  _m  x  I  _m 
volume  s  x  I      s 

Now,  supposing  this  intensity  of  magnetization  were 
due  to  the  iron  having  been  put  into  a  magnetic  field  of 
intensity  §,  the  ratio  between  the  resulting  intensity  of 
magnetization  &  and  the  magnetizing  force  §  producing 
it  is  expressible  by  a  numerical  coefficient  of  magnetization, 
or  susceptibility,  k.  We  may  write 


or  k  =  £/§. 

This  may  be  looked  at  as  saying  that  for  every  magnetic 
line  in  the  field  there  will  be  k  units  of  magnetism  on  the  end 
surface.  In  magnetic  substances  such  as  iron,  steel,  nickel, 
etc.,  the  susceptibility  k  has  positive  values ;  but  there  are 
many  substances  such  as  bismuth,  copper,  mercury,  etc., 
which  possess  feeble  negative  coefficients.  These  latter  are 
termed  "  diamagnetic  "  bodies  (Art.  398)  and  are  apparently 
repelled  by  the  poles  of  magnets.  It  was  shown  at  end  of 
Art.  365  that  there  are  4  TT  magnetic  lines  proceeding  from 
each  unit  of  pole  magnetism.  Hence  if,  as  shown  above, 
each  line  of  force  of  the  magnetizing  field  produces  k  units  of 
magnetism  there  will  be  £irk  lines  added  by  the  iron  to  each 
1  line  in  the  field,  or  the  permeability  of  the  iron  /u  is  equal 
to  1  +TT/C.  It  follows  that  33  =  §  +  47r/cg.  This  shows 
that  33  ma}'  go  on  increasing  as  long  as  §  is  increased,  having 
no  true  limit.  But  since  k  decreases  as  saturation  sets  in, 
the  intrinsic  magnetization  X  (or  $  —  §  to  which  it  is  pro- 
portional) may  have  a  true  limit.  This  maximum  of  X  appears 
to  be  about  1700  in  wrought  iron,  1250  in  cast  iron,  and  450 
in  nickel. 


CH.  v.  393]    MEASUREMENT    OF   PERMEABILITY  357 


In  the  following  table  are  given  some  figures  from  the  re- 
searches of  Bidwell  on  wrought  iron. 


$ 

k 

t 

M 

23 

3-gr 

151-0 

587 

18991 

7390 

10'3 

891 

918 

1121-4 

11550 

40 

307 

1226 

386-4 

15460 

115 

11*9 

1370 

150-7 

17330 

208 

7'0 

1452 

88-8 

18470 

427 

3'5 

1504 

45-3 

19330 

585 

2'6 

1530 

33-9 

19820 

In  weak  magnetic  fields  the  susceptibility  of  nickel  exceeds 
by  about  five  times  that  of  iron ;  but  in  strong  fields  iron  is 
more  susceptible. 

393.  Measurement  of  Permeability.  —  There  are  several 
ways  of  measuring  the  permeability  of  iron  ;  they  all  involve 
a  measurement  of  33. 

(a)  Magnetometer  Methods.  —  The  pole  strength  m  of  long 
bars,  when  magnetized  by  a  coil  around  them,  can  be  meas- 
ured by  a  magnetometer  (Art.  140),  and  from  this  g  is  found 
by  multiplying  by  4  TT  ;    and  dividing  by  the  sectional  area 
of  the  bar  gives  33. 

(b)  Induction  Methods.  —  Rings  of  iron  which,  having  no 
poles,  cannot  be  measured  by  the  magnetometer  are  measured 
inductively.     Upon  the  ring  is  wound  a  magnetizing  coil, 
and  also  an  exploring  coil  (Art.  249)  which  is  connected  to  a 
ballistic  galvanometer.     On  turning  on  or  off  the  magnetizing 
current,  or  reversing  it,  induced  currents  are  generated,  giving 
a  throw  in  the  galvanometer  proportional  to  the  number  of 
magnetic  lines  which  have  been  made  or  destroyed.      §  is 
calculated  from  the  ampere-turns  of  the  magnetizing  coil 
(Art.  368),  and  93  from  the  galvanometer  throw.     Iron  rods 
can  be  examined  by  the  same  means. 

(c)  Traction  Methods.  —  The  pull  needed  to  separate  the 
two  halves  of  a  divided  rod,  or  divided  ring,  is  (Art.  415) 
proportional  to  the  square  of  33. 


358 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  394 


(d)  Optical  Methods.  —  Du  Bois  has  used  a  method  based 
on  Kerr's  discovery  (Art.  614)  of  magneto-optirotation. 

394.  Residual  Effects.  —  The  retention  of  magnetism  by 
steel,  lodestone,  hard  iron,  and  even  by  soft  iron  if  of  elon- 
gated shape,  has  been  already  described  (Art.  101).  Some 
other  residual  effects  must  now  be  noted.  It  is  found  that 
if  a  new  piece  of  iron  or  steel  is  subjected  to  an  increasing 
magnetizing  force,  and  then  the  magnetizing  force  is  decreased 
to  zero,  some  magnetism  remains.  If  the  results  are  plotted 
out  in  a  curve  it  exhibits  the  following  peculiarities.  On 
first  gradually  increasing  §  from  0,  33 
rises  as  we  have  seen  in  Art.  391.  If 
when  the  curve  has  risen  to  a  (Fig.  202) 
§  is  now  decreased,  the  descending  curve 
does  not  follow  the  ascending  curve,  ow- 
ing to  the  retention  of  the  magnetism. 
When  §  has  been  reduced  to  zero  the 
point  b  is  reached.  This  the  residual 
value  of  S3  is  called  the  remanence,  and 
depends  on  the  material,  and  on  the  de- 
gree to  which  33  was  previously  pushed. 
The  remanence,  after  subjection  to  a  very 
strong  field,  may  be  as  high  as  10,000  in  a  ring  of  wrought 
iron  or  steel.  In  cast  iron  it  seldom  reaches  3000.  If  now 
a  reversed  magnetizing  force  —  §  is  applied  it  is  found  that 
it  must  be  increased  to  a  definite  degree  in  order  to  demag- 
netize the  iron  and  bring  the  curve  down  to  c.  The  amount 
of  reversed  magnetic  force  so  needed  is  a  measure  of  the 
retentivity  of  the  material,  and  is  known  as  the  coercive  force. 
In  hard  steel  it  may  amount  to  80;  in  soft  steel  to  20;  in 
soft  iron  to  2  or  less.  If  the  reversed  magnetizing  force  is 
further  increased,  the  curve  descends  from  c  to  d,  the  iron 
becoming  magnetized  with  reversed  polarity,  and  going  to- 
ward saturation.  On  then  diminishing  the  reversed  force 
to  zero,  the  curve  turns  to  e,  showing  a  negative  reman- 
ence. On  again  increasing  §  as  at  first  the  curve  ascends  to 


FIG.  202.  —  Cycle  of 
Magnetization. 


CH.  v.  395] 


HYSTERESIS 


359 


/,  and  as  the  former  value  of  §  is  reached  comes  up  to  a 
again. 

395.  Cycles  of  Magnetization.  Hysteresis.  —  When  § 
is  thus  carried  through  a  cycle  of  increase  and  decrease,  48 
also  goes  through  a  cycle;  and  as  we  have  seen  there  is  a 
lagging  in  the  magnetization,  evidenced  in  Fig.  202  by  the 
formation  of  a  closed  loop,  abcdefa,  in  the  curve.  Warburg 
and  Ewing,  who  have  fully  investigated  the  phenomenon, 


FIG.  203.  —  Hysteresis  Loops  for  soft  Iron  and  Steel. 

have  remarked  that  the  area  enclosed  indicates  energy  of 
waste  in  the  cycle  of  operations ;  this  energy,  seemingly  caused 
by  molecular  friction,  appearing  as  heat.  In  hard  steel  the 
areas  of  these  loops  are  much  wider  than  in  the  case  of  soft 
iron.  In  Fig.  203  are  given  the  loops  for  nearly  pure  iron  and 
a  soft  kind  of  steel.  Ewing  has  given  the  name  of  Hysteresis 
to  the  subject  of  the  lag  of  magnetic  effects  behind  their 
causes.  From  his  researches  1  also  is  taken  the  case  of  Fig. 
204,  a  specimen  of  soft  iron,  the  curve  for  which  shows  various 
partial  loops  due  to  the  removal  and  replacement  of  the 

1  The  student  should  not  fail  to  consult  Ewing's  book,  Magnetic  Induc- 
tion in  Iron. 


360 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  395 


magnetizing  force.  Ewing  has  devised  a  curve-tracer  for 
describing  the  curves  automatically.  The  waste  of  energy 
per  cubic  centimetre  in  a  cycle  of  strong  magnetization  may 
vary  from  9000  ergs  in  annealed  iron  to  200,000  in  glass-hard 
steel.  If  (as  in  the  iron  cores  of  alternate  current  transform- 
ers) the  cycle  is  repeated  50  times  a  second,  the  waste  of 

power  by  hysteresis  will  heat  the 
iron.  The  waste  increases  greatly 
with  the  frequency,  and  with  the 
degree  to  which  the  magnetiza- 
tion is  pushed.  If  23  does  not  ex- 
ceed 5000,  the  power  wasted  at 
50  cycles  per  second  in  every  cubic 
foot  of  iron  may  be  as  low  as  130 
watts,  but  if  33  is  increased  to 
10,000  the  waste  becomes  360 
watts.  In  different  kinds  of  iron, 
the  power  loss  caused  by  hyster- 
esis varies  in  a  proportion  varying 
from  S31'5  to  S32. 

Fig.  205a  shows  the  form  of  the 
hysteresis  -curves  for  very  soft 
iron  when  subjected  to  cycles  of 
magnetization  in  which  the  maxima  of  the  magnetizing  field, 
§,  are  respectively  5,  20,  and  40.  In  fields  the  intensity  of 
which  does  not  exceed  5000,  the  loop  is  practically  a  straight 
line,  there  being  no  hysteresis  waste.  Fig.  205  b  gives  for  com- 
parison three  curves  of  steel  under  similar  conditions. 

Since  a  reversed  force,  smaller  than  was  required  to 
produce  it,  suffices  to  destroy  magnetization,  all  that  is  neces- 
sary in  order  completely  to  demagnetize  iron  is  to  subject 
it  to  a  series  of  cycles  of  diminishing  intensity. 

Mechanical  agitation  tends  to  help  the  magnetizing  forces 
to  act,  and  lessens  all  residual  and  hysteresial  effects. 

Ewing  has  also  shown  that  under  constant  magnetizing 
force  the  magnetism  will  go  on  slowly  and  slightly  increasing 


FIG.  204.  —  Hysteresis  Loops. 


CH.  v.  396]      FERROMAGNETIC   SUBSTANCES 


361 


for  a  long  time :  this  is  called  magnetic  creeping,  or  viscous 
hysteresis. 

396.  Results  of  Tests ;  Ferromagnetic  Substances.  — 
The  substances  which  resemble  iron  in  magnetic  properties 
may  be  classified  thus  : 

Ferromagnetic  Elements:  iron;   cobalt;   nickel. 

Ferromagnetic  Compounds :  magnetite  (FesO,*) ;  magnetic 
pyrites  (Fe7S8) ;  ferric  antimonide  (Fe2Sb3). 

Ferromagnetic  Alloys:  Cast  iron;  the  carbon  steels;  cer- 
tain alloy  steels,  containing  various  percentages  of  carbon 


6 

3 

< 

3 

J 

5 

^- 

^ 

**— 

f 

t 

, 

•^ 

„     »* 

X 

•o  -a 

9         ' 

>         2 

D        4 

0                -4 

a    -2 

j    c 

2 

)         4 

)                -4 

>     -2 

) 

2 

0       I 

FIG.  205  a.  —  Curves  for  Soft  Iron. 


P 

<! 

5 

c 

3 

y 

^-= 

^= 

/ 

f 

-3f    o 

/ 

7 

P£    o 

( 

^ 

/ 

/ 

/ 

^M& 

•^* 

20       40  -40      -20          0         20       4O  -40      -20 

FIG.  205  b.  —  Curves  for  Steel. 


with  one  of  the  following,  tungsten,  chromium,  molybdenum, 
vanadium;  ferronickel;  ferro-chrome.  Also  Heusler's 
alloys,  such  as  the  alloy  containing  74  per  cent  of  copper, 
17  manganese,  and  9  aluminium,  which  is  as  magnetizable 
as  cast  iron ;  alloys  of  manganese  with  arsenic,  phosphorus, 
or  antimony;  and  the  alloy  of  bismuth  with  J  per  cent  of 
manganese. 

Ferromagnetic  Minerals:  A  few  minerals,  such  as  iron- 
sand,  low-grade  iron  ores,  and  tungsten  dres.  Asbestos  is 
sufficiently  magnetic  to  be  attracted  by  a  magnet.  All 


362         ELECTRICITY   AND   MAGNETISM    [PT.  n.  397,  398 

ferromagnetic  substances,  except  the  Heusler  alloys,  are 
characterized  by  having  a  high  permeability,  a  transition 
temperature  at  which  their  magnetism  disappears  (Art.  114), 
the  property  of  hysteresis  (Art.  395),  and  optical  rotatory 
power  (Art.  613).  The  alloy  steels,  particularly  tungsten  steel 
containing  about  0-5  per  cent  of  carbon  and  5  to  6  per  cent 
of  tungsten,  have  very  great  coercive  force  and  are  used  for 
permanent  magnets  (Art.  103).  Manganese  steel  is  practically 
nonmagnetic,  having  a  permeability  of  1-2  to  1-5  only. 

397.  Magnetic  Separators.  —  Advantage  is  taken  of  the 
differing  magnetic  susceptibilities  of  different  mineral  con- 
stituents to  separate  them  by  use  of  the  magnet,  the  more 
susceptible  being  more  strongly  attracted.     Machines  called 
magnetic  separators  are  used  in  which  powdered  ore  is  caused 
to  fall  or  pass  near  the  poles  of  electromagnets  or  permanent 
magnets,  which  deflect  the  more  magnetizable  constituents. 
In  this  way  low-grade  iron  ores  can  be  concentrated ;  ferru- 
ginous sands  sorted ;  the  iron  impurities  extracted  from  the 
white  sand  used  for  glass-making  or  from  the  clay  used  for 
porcelain ;   iron  filings  can  be  sorted  from  brass  filings. 

LESSON  XXIX.  —  Diamagnetism 

398.  Diamagnetic  Experiments.  —  In  1778  Brugmans  of 
Ley  den  observed  that  when  a  lump  of  bismuth  was  held 
near  either  pole  of  a  magnet  needle  it  repelled  it.     In  1827 
Le  Baillif  and  Becquerel  observed  that  the  metal  antimony 
also  could  repel  and  be  repelled  by  the  pole  of  a  magnet. 
In  1845  Faraday,  using  powerful  electromagnets,  examined 
the  magnetic  properties  of  a  large  number  of  substances,  and 
found  that  whilst  a  great  many  are,  like  iron,  attracted  to 
a  magnet,  others  are  feebly  repelled.     To  distinguish  between 
these  two  classes  of  bodies,  he  termed  those  which  are  at- 
tracted paramagnetic,  and  those  which  are  repelled  diamag- 
netic.     The  property  of  being  thus  apparently  repelled  from 
a  magnet  he  termed  diamagnetism. 


CH.  V. 


DIAMAGNETISM 


363 


Faraday's  method  of  experiment  consisted  in  suspending  a 
small  bar  of  the  substance  in  a  powerful  magnetic  field  be- 
tween the  two  poles  of  an  electromagnet,  and  observing 
whether  the  small  bar  was  attracted  into  an  axial  position, 
as  in  Fig.  206,  with  its  length  along  the  line  joining  the  two 
poles,  or  whether  it  was  repelled  into  an 
equatorial  position,  at  right  angles  to  the 
line  joining  the  poles,  across  the  lines  of 
force  of  the  field,  as  is  shown  by  the  posi- 
tion of  the  small  bar  in  Fig.  207,  sus- 
pended between  the  poles  of  an  elec- 
tromagnet constructed  on  RuhmkorfPs 
pattern. 

Liquids  were  placed  in  glass  vessels 
and  suspended  between  the  poles  of  the 
electromagnet.      Almost  all  liquids  are 
diamagnetic,  except  solutions  of  salts  of  the  magnetic  metals, 
some  of  which  are  feebly  magnetic ;    but  blood  is  diamag- 


FIG.  206. —  Axil  Position 
assumed  by  a  Paramag- 
netic Bar. 


PIG.  207.  —  Equatorial  Position  assumed  by  a  Diamagnetic  Bar. 

netic  though  it  contains  iron.  To  examine  gases,  bubbles 
were  blown  with  them,  and  watched  as  to  whether  they  were 
drawn  into  or  pushed  out  of  the  field.  Oxygen  gas  was  found 


364 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  399 


to  be  magnetic ;  ozone  has  been  found  to  be  still  more  strongly 
so.  Dewar  found  liquid  oxygen  sufficiently  magnetic  to  rush 
in  drops  to  the  poles  of  a  powerful  magnet. 

399.  Paramagnetic  and  Diamagnetic  Data.  —  In  these 
two  classes  of  feebly  magnetic  bodies  the  permeability,  /x, 
scarcely  differs  from  that  of  air.  In  the  most  paramagnetic, 
the  rare  metal  erbium,  /*  =  1-00289;  in  the  most  diamag- 
netic,  bismuth,  /x  =  0-999824.  It  is  more  convenient  to 
state  their  properties  in  terms  of  the  susceptibility  k  (Art. 
392),  which  for  air  is  zero,  and  is  negative  for  the  diamagnetic 
bodies.  The  following  table  gives  a  list  of  elements,  the  num- 
bers given  being  the  values  of  A:  X  106. 


Erbium            +  231 

Tin,    Silicon,   Potassium, 

Cerium             +182 

Sodium,  Calcium,  and 

Didymium       +121 

Barium      are      almost 

Lanthanum     +112 

neutral. 

0 

Thorium          +    81 

Phosphorus  —    0'4 

'•+3 
o 

Palladium        +    58 

o 

'•£ 

Copper          -    0'66 

Tantalum        +    58 

0 

B 

Zinc               -    0'8 

a  ' 

Platinum         +    29 

to 

Oj    ' 

Lead              -    1'36 

eS 

Uranium          +    16 

1 

Silver             -    1'6 

S 

Titanium         +    14 

IB 

Carbon          -    2  '5 

P-i 

Tungsten         +    12 

Gold               -    2'8 

Manganese  1    +    10 

Thallium       -    4'6 

Chromium       +      4 

Mercury        —    2  '6 

Molybdenum  +      2 

Antimony      —    3'8 

Aluminium      +      2 

Bismuth        -  14'0 

The  characteristic  of  paramagnetic  bodies  is  that  in  them 
the  permeability  is  small ;  they  exhibit  no  hysteresis ;  they 
have  no  transition  temperature,  but  follow  Curie's  law  that 
their  susceptibility  varies  inversely  as  the  absolute  tem- 
perature. Most  of  the  salts  of  the  ferromagnetic  bodies, 
for  example  the  salt  of  iron,  are  paramagnetic,  except  where 
the  iron  constituent  is  in  the  acidic  radicle,  as  in  the 
ferrocyanides,  which  are  practically  neutral. 

1  But  manganese  fused  in  an  electric  furnace  is  said  to  be  ferromagnetic 
with  a  maximum  magnetization  about  1  per  cent  of  that  of  iron. 


CH.  v.  400]  DIAMAGNETIC   POLARITY  365 

It  is  found  that  feebly  magnetic  bodies,  when  suspended 
in  a  more  highly  magnetic  medium,  behave  as  if  they  were 
diamagnetic.  A  small  glass  tube  filled  with  a  weak  solution 
of  ferric  chloride,  when  suspended  in  air  between  the  poles 
of  an  electromagnet,  points  axially,  or  is  paramagnetic; 
but  if  it  be  surrounded  by  a  stronger  (and  therefore  more 
magnetic)  solution  of  the  same  substance,  it  points  equato- 
rially,  and  is  apparently  repelled  like  diamagnetic  bodies. 
All  that  the  equatorial  pointing  of  a  body  proves  then  is, 
that  it  is  less  magnetic  than  the  medium  that  fills  the  sur- 
rounding space.  A  balloon,  though  it  possesses  mass  and 
weight,  rises  through  the  air  in  obedience  to  the  law  of  gravity, 
because  the  medium  surrounding  it  is  more  attracted  than  it 
is.  But  it  is  found  that  diamagnetic  repulsion  takes  place 
even  in  a  vacuum :  hence  it  would  appear  that  the  ether  of 
space  itself  is  more  magnetic  than  the  substances  classed 
as  diamagnetic.  The  susceptibility  of  air  as  compared  with 
that  of  vacuum  appears  to  be  about  +  0-000000023;  that 
of  water  +  0-000000804. 

400.  Diamagnetic  Polarity.  —  At  one  time  Faraday 
thought  that  diamagnetic  repulsion  could  be  explained  on 
the  supposition  that  there  existed  a  "  diamagnetic  polar- 
ity," the  reverse  of  the  ordinary  magnetic  polarity.  Ac- 
cording to  this  view  (which,  however,  Faraday  himself  quite 
abandoned),  a  magnet,  when  its  N-pole  is  presented  to  the 
end  of  a  bar  of  bismuth,  induces  in  that  end  a  N-pole  (the 
reverse  of  what  it  would  induce  in  a  bar  of  iron  or  other 
magnetic  metal),  and  therefore  repels  it.  Weber  adopted 
this  view,  and  Tyndall  warmly  advocated  it,  especially  after 
discovering  that  the  repelling  diamagnetic  force  varies  as  the 
square  of  the  magnetic  power  employed.  It  has  even  been 
suggested  that  when  a  diamagnetic  bar  lies  equatorially  across 
a  field  of  force,  its  east  and  west  poles  possess  different  prop- 
erties. The  experiment  named  above  suggests,  however,  an 
explanation  less  difficult  to  reconcile  with  the  facts.  It  has 
been  pointed  out  (Art.  390)  that  the  degree  to  which  magneti- 


366  ELECTRICITY  AND   MAGNETISM         [PT.  n.  401 

zation  goes  on  in  a  medium  depends  upon  the  magnetic 
permeability  of  that  medium.  Now,  permeability  expresses 
the  number  of  magnetic  lines  induced  in  the  medium  for  every 
line  of  magnetizing  force  applied.  A  certain  magnetizing 
force  applied  to  a  space  containing  air  or  vacuum  would  in- 
duce a  certain  number  of  magnetic  lines  through  it.  If  the 
space  considered  were  occupied  by  a  paramagnetic  substance 
it  would  concentrate  the  magnetic  lines  into  itself,  as  the 
sphere  does  in  Fig.  208  a.  But  if  the  sphere  were  of  a  per- 
meability less  than  1,  the  magnetic  lines  would  tend  rather 
to  pass  through  the  air,  as  in  Fig.  208  b.  If  the  space  con- 
sidered were  occupied  by  bismuth,  the  same  magnetizing- 


FIG.  208  a.  —  Paramagnetic  Body.          FIG.  208  b.  —  Diarnagnetic  Body. 

force  would  induce  in  the  bismuth  fewer  magnetic  lines  than 
in  a  vacuum.  But  those  lines  which  were  induced  would 
still  run  in  the  same  general  direction  as  in  the  vacuum; 
not  in  the  opposite  direction,  as  Weber  and  Tyndall  main- 
tained. The  result  of  there  being  a  less  dense  flux  through 
diamagnetic  substances  can  be  shown  to  be  that  such  sub- 
stances will  be  urged  from  places  where  the  magnetic  force 
is  strong  to  places  where  it  is  weaker.  This  is  why  a  ball  of 
bismuth  moves  away  from  a  magnet,  and  why  a  little  bar 
of  bismuth  between  the  conical  poles  of  the  electromagnet 
(Fig.  207)  turns  equatorially  so  as  to  put  its  ends  into  the 
regions  that  are  magnetically  weaker.  There  is  no  reason 
to  doubt  that  in  a  magnetic  field  of  uniform  strength  a  bar 
of  bismuth  would  point  along  the  magnetic  lines. 

401.  Magne-Crystallic  Action.  —  In  1822  Poisson  pre- 
dicted that  a  body  possessing  crystalline  structure  would, 
if  magnetic  at  all,  have  different  magnetic  powers  in  different 


CH.  v.  402]          DIAMAGNETISM    OF   FLAMES  367 

directions.  In  1847  Pliicker  discovered  that  a  piece  of  tour- 
maline, which  is  itself  feebly  paramagnetic,  behaved  as  a  dia- 
magnetic  body  when  so  hung  that  the  axis  of  the  crystal 
was  horizontal.  Faraday,  repeating  the  experiment  with  a 
crystal  of  bismuth,  found  that  it  tended  to  point  with  its 
axis  of  crystallization  along  the  lines  of  the  field  axially. 
The  magnetic  force  acting  thus  upon  crystals  by  virtue  of 
their  possessing  a  certain  structure  he  named  magne-crystallic 
force.  Pliicker  endeavoured  to  connect  the  magne-crystallic 
behaviour  of  crystals  with  their  optical  behaviour,  giving 
the  following  law :  there  will  be  either  repulsion  or  attraction 
of  the  optic  axis  (or,  in  the  case  of  bi-axial  crystals,  of  both 
optic  axes)  by  the  poles  of  a  magnet ;  and  if  the  crystal  is  a 
"  negative  "  one  (i.e.  optically  negative,  having  an  extraor- 
dinary index  of  refraction  less  than  its  ordinary  index) 
there  will  be  repulsion,  but  if  a  "  positive  "  one  there  will  be 
attraction.  Tyndall  endeavoured  to  show  that  this  law  is 
insufficient  in  not  taking  into  account  the  paramagnetic 
or  diamagnetic  powers  of  the  substance  as  a  whole.  He 
found  that  the  magne-crystallic  axis  of  bodies  is  in  general 
an  axis  of  greatest  density,  and  that  if  the  mass  itself  be  para- 
magnetic this  axis  will  point  axially;  if  diamagnetic,  equatori- 
ally.  In  bodies  which,  like  slate  and  many  crystals,  possess 
cleavage,  the  planes  of  cleavage  are  usually  at  right  angles 
to  the  magne-crystallic  axis.  Another  way  of  stating  the 
facts  is  to  say  that  in  non-isotropic  bodies  the  induced  mag-' 
netic  lines  do  not  necessarily  run  in  the  same  direction  as  the 
lines  of  the  impressed  magnetic  field.  In  natural  crystals 
of  magnetite  the  magnetic  susceptibility  is  a  maximum  in  the 
four  directions  normal  to  the  octahedral  faces.  Pyrrhotine, 
Fe7O8,  is  non-magnetic  along  the  axis,  but  strongly  para- 
magnetic transversely. 

402.  Diamagnetism  of  Flames.  —  In  1847  Bancalari 
discovered  that  flames  are  repelled  from  the  axial  line  joining 
the  poles  of  an  electromagnet.  Faraday  showed  that  all 
kinds  of  flames,  as  well  as  ascending  streams  of  hot  air  and  of 


368  ELECTRICITY  AND   MAGNETISM       [PT.  n.  403 

smoke,  are  acted  on  by  the  magnet,  and  tend  to  move  from 
places  where  the  magnetic  forces  are  strong  to  those  where 
they  are  weaker.  Gases  (except  oxygen  and  ozone),  and  hot 
gases  especially,  are  feebly  diamagnetic.  But  the  active  re- 
pulsion and  turning  aside  of  flames  may  possibly  be  in  part 
due  to  an  electromagnetic  action  like  that  which  the  magnet 
exercises  on  the  convection-current  of  the  voltaic  arc  (Art. 
429)  and  on  other  convection-currents.  The  electric  proper- 
ties of  flame  are  mentioned  in  Arts.  9  and  334. 


LESSON  XXX.  —  The  Magnetic  Circuit 

403.  Magnetic  Circuits.  —  A  magnetic  circuit  consists 
generally  of  a  number  of  portions,  iron  or  air,  through  which 
the  magnetic  flux  passes.  Sometimes  it  consists  of  a  core 
of  iron  only,  in  the  form  of  a  ring  ;  sometimes  it  consists  of 
air  only  ;  more  often,  as  in  all  electromagnets,  of  an  iron  core 
with  air-gaps  between  its  parts.  There  is  a  magnetic  circuit 
law  similar  to  the  law  of  Ohm  for  electric  circuits.  Ritchie, 
Sturgeon,  Joule,  and  Faraday  dimly  recognized  it.  But  the 
law  was  first  put  into  shape  in  1873  by  Rowland,  who  calcu- 
lated the  flow  of  magnetic  lines  through  a  bar  by  dividing 
the  "  magnetizing  force  of  the  helix  "  by  the  "  resistance  to 
lines  of  force  "  of  the  iron.  In  1882  Bosanquet  introduced 
the  term  magnetomotive-force,  and  showed  how  to  calculate 
the  reluctances  of  the  separate  parts  of  the  magnetic  circuit, 
and,  by  adding  them,  to  obtain  the  total  reluctance.1 

The  law  of  the  magnetic  circuit  may  be  stated  as  follows  :  — 

Magnetic  Flux  =  magnetomotive-force 
reluctance 


1  This  useful  term,  far  preferable  to  "magnetic  resistance,"  was  intro- 
duced by  Oliver  Heaviside.  The  term  reluctivity  is  sometimes  used  for  the 
specific  reluctance  ;  it  is  the  reciprocal  of  permeability. 


CH.  v.  404]  RELUCTANCE  369 

The  magnetomotive-force  is,  as  shown  in  Art.  368,  depen- 
dent on  the  strength  of  the  current  and  on  the  number  of 
turns  by  which  it  is  interlinked  with  the  magnetic  circuit. 
Formerly  it  was  usual  to  give  the  name  of  magnetomotive- 

4  TT 
force  to  — —  times  the  number  of  ampere-turns  (see  Art.  368) ; 

but  in  modern  usage  the  ampere-turns  themselves  are  taken 

4  7T 

as  the  magnetomotive-force,  and  the  numeric  — —  then  comes 

as  a  divisor  into  the  calculation  of  the  reluctance. 

404.  Reluctance.  —  As  the  electric  resistance  of  a  pris- 
matic conductor  can  be  calculated  from  its  length,  cross- 
section,  and  conductivity,  so  the  magnetic  reluctance  of  a 
bar  of  iron  can  be  calculated  from  its  length,  cross-section, 
and  permeability.  The  principal  difference  between  the  two 
cases  lies  in  the  circumstance  that  whilst  in  the  electric  case 
the  conductivity  is  the  same  for  small  and  large  currents,  in 
the  magnetic  case  the  permeability  is  not  constant,  but  is 
less  for  large  magnetic  fluxes  than  for  small  ones. 

Let  the  length  of  the  bar  be  I  centims.,  its  section  A  sq.  cms., 
and  its  permeability  /u.  Then  its  reluctance  will  be  propor- 
tional directly  to  I,  and  inversely  to  A  and  /x..  Calling  the 
reluctance  Z  we  have 

Z       jL.i.i£. 
A/*  '    10  ' 

or  Z  =  ~  X  0796. 

A/A 

Example.  —  An  iron  bar  100  cm.  long  and  4  sq.  cms.  in  cross- 
section  is  magnetized  to  such  a  degree  that  M  =  320 : 
then  Z  will  be  0.062. 

The  reluctance  of  a  magnetic  circuit  is  generally  made 
up  of  a  number  of  reluctances  in  series.  We  will  first  take 
the  case  of  a  closed  magnetic  circuit  (Fig.  209  a)  made  up  of 
a  curved  iron  core  of  length  ll}  section  AI,  and  permeability  /AI  ; 
and  an  armature  of  length  12,  section  A2,  and  permeability  /A2, 
2n 


370  ELECTRICITY   AND   MAGNETISM       [PT.  n.  405 

in  contact  with  the  ends  of  the  former.     In  this  case  the  re- 
luctance i 

Z  =l_+--x0796. 


To  the  reciprocal  of  the  reluctance  the  name  of  the  per- 
meance is  sometimes  given. 

405.  Calculation  of  Excitation.  —  Passing  on  to  the  more 
difficult  case  of  a  circuit  made  up  partly  of  iron  and  partly 
of  air,  we  will  suppose  the  armature  to  be  moved  to  a  dis- 
tance, so  that  there  are  two  air-gaps  (Fig.  209  6)  in  the  circuit, 


FIG.  209  a.  —  Electromagnet,  with  FIG.  209  6.  —  Electromagnet,  with 

closed  Magnetic  Circuit.  Gaps  in  the  Magnetic  Circuit. 

each  gap  of  length  /3  (from  iron  to  iron),  and  section  A3 
(equal  to  area  of  pole  face).  This  will  introduce  an  addi- 
tional reluctance  2  Z3/A3,  the  permeability  for  air  being  =  1. 
It  will  also  have  the  effect  of  making  part  of  the  magnetic 
flux  leak  out  of  the  circuit.  Magnetic  leakage  is  due  to  the 
circumstance  that  the  permeability  of  air  is  not  zero,  but 
unity,  and  therefore  part  of  the  flux  passes  uselessly  from  pole 
to  pole  through  the  air.  That  part  of  the  whole  flux  which 
thus  leaks  across  instead  of  going  usefully  into  the  armature 
is  called  the  stray  flux. 

By  Art.  368,  if  the  excitation  consists  of  i  amperes  circulat- 
ing in  S  spirals  around  the  core,  the  magnetomotive-force  will 
be  iS.  Applying  this  to  the  preceding  example,  dividing  the 
magnetomotive-force  by  the  reluctance,  we  get  for  the  mag- 
netic flux  —  - 


jm 

4 


7T 


l\      i     li      ,  2  Z3 
r- h  -T— 

A3 


CH.  v.  405]      CALCULATION   OF   EXCITATION  371 

But  more  often  the  calculation  is  wanted  the  other  way 
round,  to  find  how  many  ampere-turns  of  excitation  will 
be  needed  to  produce  a  given  flux  through  a  magnetic  circuit 
of  given  size.  Two  difficulties  arise  here.  The  permeability 
will  depend  on  the  degree  of  saturation,  that  is  to  say,  on  the 
flux-density  in  the  iron.  Also  the  leakage  introduces  an 
error.  To  meet  the  first  difficulty  approximate  values  of  /x 
must  be  found.  Suppose,  for  example,  it  was  intended  to 
produce  a  flux  of  1,000,000  lines  through  an  iron  bar  having 
a  section  of  80  sq.  centims.,  then  33  will  be  12,500,  and  ref- 
erence to  the  table  in  Art.  391  shows  that  if  the  bar  is  of 
wrought  iron  /x  will  be  about  1247.  To  meet  the  second 
difficulty  we  must  estimate  (from  experience)  an  allowance 
for  leakage.  Suppose  we  find  that  of  all  the  lines  created  in 
the  U-shaped  part  only  the  fraction  l/v  gets  through  the 
armature,  then  to  force  g  lines  through  the  armature  we 
must  generate  v$  lines  in  the  U-shaped  piece,  where  v  is  the 
coefficient  of  allowance  for  leakage,  an  improper  fraction 
increasing  with  the  width  of  the  gaps. 

We  then  proceed  to  calculate  in  parts  as  follows  :  - 

Ampere-  turns  needed  to  drive  v%  lines  1  _  ^  x    h    _._  1-257 

through  iron  of  magnet  core  J  AI/*I 

Ampere-turns  needed  to  drive  ft  lines  1  _  <*      2  13  ^_  *  .9tV7 

,  i  i     ,  f  '  —  ?\  /\     i       •    -*•  ^O  i  • 

through  two  gaps  A3 

Ampere-turns  needed  to  drive  ft  lines  j  _      ^    k        i'2(57 
through  iron  of  armature  j  ,  ' 


Then  adding  up,  we  get  :  — 

Total  ampere-  turns  needed       =  ft  (  -^i-+  -A_  +  2j?  j  +  ^257 

{  AI/XI       A2At2       A3  j 

Formulae  similar  to  this  were  introduced  by  Hopkinson 
and  by  Kapp  in  designing  electromagnets  for  dynamos. 
But  it  is  possible  to  simplify  them  by  remembering  that 
if  a  flux  g  passes  through  an  area  of  cross-section  A,  the 
flux-density  53  can  be  found  by  dividing  g  by  A.  And 
if  we  know  what  the  value  of  53  is  going  to  be,  then  we 
can  find  the  corresponding  value  of  the  ampere-turns  per 


372  ELECTRICITY   AND   MAGNETISM       [PT.  n.  406 

centimetre  from  Tables,  or  from  the  corresponding  curves 
(Art.  391),  for  the  brand  of  iron  concerned,  and  can  multiply 
the  values  so  found  by  the  number  of  centimetres'  length  of 
that  part. 

Example.  —  An  electromagnet  having  for  its  U-shaped  core  of 
wrought  iron  a  length  of  24  cm.  and  a  cross-section  of  4'8 
sq.  cms.  is  lightly  chamfered  to  have  the  area  of  each  pole 
4'0  sq.  cms.  The  wrought-iron  armature  is  wide  enough 
to  cover  the  pole  surfaces  ;  the  mean  length  of  path  through 
it  is  5  cm.  and  its  section  3  sq.  cms.  Find  the  ampere- 
turns  needed  to  produce  a  flux  of  36,000  lines  through  the 
armature  when  the  air-gaps  are  each  1  mm.  Assume  v 
=  1-36.  Here  k  =  5  ;  12  =  O'l ;  Z3  =  24  ;  AI  =  3  ;  A2  =  4  ; 
A3  =  4*8.  If  &  =  36,000,  $!  =  12,000.  Hence,  from  the 
curve  in  Fig.  200,  or  by  the  Table  on  p.  355,  we  see  that 
each  centimetre  of  armature  length  will  require  9  ampere- 
turns  ;  or  the  ampere-turns  needed  for  the  armature  will 
be  45.  In  the  air-gaps  the  flux-density  is  $•  -f-  4  =  9000 ; 
and,  dividing  by  1*257,  we  find  that  each  centimetre- 
length  in  air  will  therefore  read  7159  ampere- turns ; 
hence,  as  total  air-gap  length  is  0'2  cm.  the  ampere-turns 
needed  for  that  part  are  143T8.  The  flux  through  the 
core  will  be  1'36  X  36,000  =  48,960;  the  density  in  the 
core  will  be  10,200;  whence,  by  the  Table  or  the  curves 
of  Fig.  201,  the  ampere- turns  needed  per  centimetre  length 
will  be  6*2.  So  the  ampere-turns  for  the  24  cm.  length 
will  be  153-6.  Adding  up,  45  +  1431  -8  +  153'6  =  1630 
total  ampere-turns  needed  for  the  magnetic  circuit. 

406.  Effect  of  Air-Gap  in  Circuit.  —  Air  having  no  rema- 
nence,  the  presence  of  a  gap  in  the  iron  circuit  tends  to 
make  residual  magnetism  unstable,  as  though  the  polar 
magnetism  on  the  end-faces  had  a  self-demagnetizing  effect. 
In  fact  it  is  very  difficult  to  give  a  permanent  magnetism  to 
short  pieces  of  steel.  Further,  the  low  permeability  of  air 
necessitates  enormous  magnetomotive-forces,  compared  with 
those  required  for  iron,  to  force  a  given  flux  across  a  gap. 
The  effect  is  to  shear  over  to  the  right  the  curves  of  mag- 
netization, seeing  that  a  greater  §  is  needed  to  attain  an  equal 
value  of  33.  Joints  in  the  magnetic  circuit  act  as  narrow  gaps. 

The  chief  reason  why  the  pull  exerted  by  an  electromag- 


CH.  v.  407-409]  PULL   OF   ELECTROMAGNETS  373 

net  on  its  keeper  falls  off  so  very  greatly  when  the  keeper  is 
moved  away  to  a  short  distance  is  the  diminution  of  the  mag- 
netic flux  caused  by  the  great  reluctance  of  the  air-gap  thus 
introduced  into  the  circuit. 

407.  Contrast   between   Electromagnets   and   Permanent 
Magnets.  —  It  is  found  that  with  electromagnets  the  pull 
on  the  keeper,  when  the  keeper  is  removed  to  a  given  dis- 
tance, falls  off  more  rapidly  than  is  the  case  with  permanent 
magnets.     The  reason  is  that  with  permanent  magnets  the 
flux  remains  constant,  while  with  electromagnets  the  increase 
of  the  reluctance  of  the  air-gap  causes  the  flu*  in  the  magnetic 
circuit  to  diminish ;    so  that  there  are  two  causes  at  work : 
(i.)  diminution  of  flux;  (ii.)  the  leakage  of  the  stray  flux 
from  pole  to  pole.     Let  the  reader  compare  Fig.  91,  p.  126, 
with  Fig.  210,  p.  374. 

408.  Magnetic   Shunts.  —  If  a  magnetic   circuit  divides 
at  any  place  into  two  paths  part  of  the  flux  goes  along  each 
path.     The  two  paths  being  in  parallel  with  one  another 
the  relative  fraction  of  the  flux  which  traverses  each  will  be 
inversely  proportional  to  their  respective  reluctances.     A 
piece  of  iron  placed  so  as  to  divert  a  portion  of  the  flux  is 
termed  a  magnetic  shunt. 

409.  General  Law  of  Electromagnetic   Systems.  —  Con- 
sider an  electromagnetic  system  consisting  of  any  number 
of  parts  —  iron  masses,  coils  carrying  currents,  air,  masses 
of  other  materials,  whether  magnetic  or  diamagnetic  —  in 
any  given  configuration.     Any  change  in  the  configuration 
of  the  parts  will  in  general  produce  either  an  increase  or  a 
decrease  in  the  magnetic  flux.     For  example,  if  the  armature 
of  an  electromagnet  is  allowed  to  move  up  toward  the  poles, 
or  if  the  needle  of  a  galvanometer  is  allowed  to  turn,  there  will 
be  a  betterment  of  the  magnetic  circuit,  and  the  magnetic 
flux  through  the  coils  will  be  increased.     Magnetic  circuits 
always  tend  to  close  up  and  become  as  compact  as  possible. 
On  the  contrary,  if  we  pull  away  the  armature  from  an  elec- 
tromagnet the  magnetic  reluctance  is  increased,  and  the  flux 


374 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  409 


diminished  ;  and  this  action  is  resisted  by  the  reaction  of  the 
system.  All  these  things  may  be  summed  up  in  the  following 
general  law :  — 


Every  electromagnetic  system  tends  so  to  change  the  con- 
figuration of  its  parts  as  to  make  the  interlinkage  of  the  mag- 
netic flux  throygh  the  exciting  coils  a  maximum. 


CH.  v.  410]         LAW   OF   MAGNETIC    CIRCUIT  375 

Suppose  (the  exciting  ampere-turns,  iS,  remaining  the 
same)  a  motion  of  any  part  through  a  distance  dx  to  result 
in  a  decrease  of  flux  d$,  then  the  force  resisting  such  motion 
will  be  proportional  to 


410.  Empirical  Rules.  —  Before  the  law  of  the  magnetic  circuit 
was  understood  many  attempts  were  made  to  find  algebraic  formulae 
to  express  the  relation  between  the  strength  of  current  and  the 
amount  of  magnetism  produced.  Lenz  and  Jacobi  suggested  that 
the  magnetism  of  an  electromagnet  was  proportional  to  the  current 
and  to  the  number  of  turns  of  wire  in  the  coil  —  in  other  words,  is 
proportional  to  the  ampere-turns.  Or,  in  symbols, 

m  =  aiS, 

where  a  is  a  constant  depending  on  the  quantity,  quality,  and  form 
of  iron.  This  rule  is,  however,  only  true  when  the  iron  core  is 
still  far  from  being  "  saturated."  If  the  iron  is  already  strongly 
magnetized  a  current  twice  as  strong  will  not  double  the  magnetiza- 
tion in  the  iron,  as  Joule  showed  in  1847. 

Miiller  gave  the  following  approximate  rule  :  —  The  strength  of 
an  electromagnet  is  proportional  to  the  angle  whose  tangent  is  the 
strength  of  the  magnetizing  current  ;  or 

m  =  A  tan~H', 

where  i  is  the  magnetizing  current,  and  A  a  constant  depending 
on  the  eonstruction  of  the  particular  magnet.  If  the  student  will 
look  at  Fig.  133  and  imagine  the  divisions  of  the  horizontal  tangent 
line  OT  to  represent  strengths  of  current,  and  the  number  of  de- 
grees of  arc  intercepted  by  the  oblique  lines  to  represent  strengths 
of  magnetism,  he  will  see  that  even  if  OT  be  made  infinitely  long, 
the  intercepted  angle  can  never  exceed  90°. 
Another  formula,  known  as  Frolich's,  is  — 

i 

m  =  a  i    .  ,  .. 
1  +  bi 

where  a  and  6  are  constants  depending  on  the  form,  quality,  and 
quantity  of  the  iron,  and  on  the  winding  of  the  coil.  The  constant 
b  is  the  reciprocal  of  that  number  of  amperes  which  would  make 
m  equal  to  half  possible  maximum  of  magnetism. 

The  author's  variety  of  this  formula  expresses  the  number  of 
magnetic  lines  $  proceeding  from  the  pole  of  the  electromagnet  — 

cc       v       ^ 

=  Y 


376 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  411 


where  Y  represents  the  maximum  number  of  magnetic  lines  that 
there  would  be  if  the  magnetizing  current  were  indefinitely  increased 
and  the  iron  core  saturated,  and  i'  stands  for  that  number  of  amperes 
which  would  bring  the  magnetism  up  to  half-saturation. 

None  of  these  empirical  formulae  are  as  useful  as  the  rational 
formula  at  the  end  of  Art.  405. 


LESSON  XXXI.  —  Electromagnets 

411.  Electromagnets.  —  In  1820,  almost  immediately 
after  Oersted's  discovery  of  the  action  of  the  electric  current 
on  a  magnet  needle,  Arago  and  Davy  independently  dis- 
covered how  to  magnetize  steel  and  iron  by  inserting  needles 
or  strips  into  spiral  coils  of  copper  wire  around  which  a  cur- 


Fid.  211.  —  Magnetization  of  Bar  of  Iron,  by  Circulation  of  Current. 

rent  was  circulating.  The  method  is  shown  in  the  simple 
diagram  of  Fig.  211,  where  a  current  from  a  single  cell  is 
passed  through  a  spiral  coil  of  insulated  copper  wire,  in  the 
hollow  of  which  is  placed  a  strip  of  iron  or  steel,  which  is 
thereby  magnetized.  The  separate  turns  of  the  coil  must  not 
touch  one  another  or  the  central  bar,  otherwise  the  current 
will  take  the  shortest  road  open  to  it  and  will  not  traverse  the 
whole  of  the  coils.  To  prevent  such  short-circuiting  by  con- 
tact the  wire  of  the  coil  should  be  overspun  with  silk  or  cotton 
(in  the  latter  case  insulation  is  improved  by  varnishing  it 
or  by  steeping  the  cotton  covering  in  melted  paraffin  wax) 


CH.  v.  412] 


ELECTROMAGNETS 


377 


FIG.  212.  —  Sturgeon's 
Electromagnet  (1825). 


or  covered  with  a  layer  of  enamel.  If  the  bar  be  of  soft 
iron  it  will  be  a  magnet  only  so  long  as  the  current  flows; 
and  an  iron  core  thus  surrounded  with  a  coil  of  wire  for  the 
purpose  of  magnetizing  it  by  an  electric  current  is  called  an 
Electromagnet.  Sturgeon,  who  gave  this  name,  applied  the 
discoveries  of  Davy  and  Arago  to  the  construction  of  elec- 
tromagnets far  more  powerful  than  any  magnets  previously 
made.  His  first  electromagnet  was  a  horse-shoe  (Fig.  212) 
made  of  a  rod  of  iron  about  1  foot  long  and  J  inch  in  diameter 
coiled  with  a  single  stout  copper  wire  of  only 
18  turns.  With  the  current  from  a  single 
cell  it  lifted  9  Ibs. ;  but  with  a  more  power- 
ful battery  it  lifted  50  Ibs.  It  was  first 
shown  by  Henry  that  when  electromagnets 
are  required  to  work  at  the  distant  end  of 
a  long  line  they  must  be  wound  with  many 
turns  of  fine  wire.  The  great  usefulness  of 
the  electromagnet  in  its  application  to  electric  bells  and  the 
telegraphic  instruments  lies  in  the  fact  that  its  magnetism 
is  under  the  control  of  the  current;  when  circuit  is  "  made  " 
it  becomes  a  magnet,  when  circuit  is  "  broken  "  it  ceases  to 
act  as  a  magnet.  Moreover,  it  is  capable  of  being  controlled 
from  a  distance,  the  current  being  "  made  "  or  "  broken  " 
at  a  distant  point  of  the  circuit  by  a  suitable  key  or  switch. 

412.  Polarity  and  Circulation  of  Current.  —  By  applying 
Ampere's  Rule  (Art.  210)  we  can  find  which  end  of  an  elec- 
tromagnet will  be  the  N-seeking  pole ; 
for,  imagining  ourselves  to  be  swim- 
ming in  the  current  (Fig.  211),  and 
to  face  towards  the  centre  where 

FIG.  213. -Connexion  of  Polar-     the    il>On    bai>    is>   the    N-SCeking    pole 

ity  with  Direction  of  circuia-    w{\\  be  on  the  left.     It  is  convenient 

tion. 

to  remember  this  relation  by  the  fol- 
lowing rules :  —  Looking  at  the  S-seeking  pole  of  an  electro- 
magnet, the  magnetizing  currents  are  circulating  round  it  in 
the  same  cyclic  direction  as  the  hands  of  a  clock  move;  and, 


378 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  413 


looking  at  the  N-seeking  pole  of  an  electromagnet,  the  mag- 
netizing currents  are  circulating  round  it  in  the  opposite  cyclic 
direction  to  that  of  the  hands  of  a  clock. 
Fig.  213  shows  this  graphically.  These 
rules  are  true,  no  matter  whether  the  be- 
ginning of  the  coils  is  at  the  end  near  the 
observer,  or  at  the  farther  end  from  him, 
i.e.  whether  the  spiral  be  a  right-handed 
screw,  or  (as  in  Fig.  211)  a  left-handed 
screw.  It  will  be  just  the  same  thing,  so 
far  as  the  magnetizing  power  is  concerned. 

FIG.  214.  —  Consequent  .  , 

Poles  in  a  Ring-Eiec-  if  the  coils  begin  at  one  end  and  run  to  the 
tromagnet.  ot her  and  back  ^  wbere  t ^ey  began ;  or  they 

may  begin  half-way  along  the  bar  and  run  to  one  end  and  then 
back  to  the  other ;  the  one  important  thing  to  know  is  which 
way  the  current  flows  round  the  bar  when  you  look  at  it  end- 
on.  The  cork-screw  rule  (Art.  211)  leads  to  the  same  result. 

Suppose  an  iron  core  to  be  wound  with  a  right-handed 
coil,  and  that  a  current  is  introduced  at  some  point,  and  to 
flow  both  ways,  it  will  produce  oppositely-directed  magnetiz- 
ing actions  in  the  two  points,  and  there  will  be  consequent 
poles  (Art.  122)  at  the  point  of  entrance.  In  Fig.  214  an  iron 
ring  with  a  right-handedly-wound 
closed  coil  is  shown.  There  will  be 
a  double  S-pole  at  the  point  where 
the  current  enters,  and  a  double  N- 
pole  where  it  leaves  the  windings. 

413.  Construction  of  Electromag- 
nets. —  The  most  useful  form  of 
electromagnet  is  that  in  which  the 
iron  core  is  bent  into  the  form  of  a 
horse-shoe,  so  that  both  poles  may 
be  applied  to  one  iron  armature.  In 
this  case  it  is  usual  to  divide  the  coils  into  two  parts  wound 
on  bobbins,  as  in  Figs.  68  and  215.  Often  the  iron  part  is 
made  of  two  straight  limbs  fixed  into  a  cross-piece  or  yoke. 


FIG.  215.  —  A  Horse-shoe 
Electromagnet. 


CH.  v.  413]        FORMS   OF   ELECTROMAGNETS 


379 


Sometimes  only  one  coil  is  wound  on  the  yoke  part.  The 
electromagnet  depicted  in  Fig.  216  is  of  a  form  adapted  for 
laboratory  experiments,  and  has  movable  coils  which  are 
slipped  on  over  the  iron  cores.  As  a  rule  the  iron  parts,  in- 
cluding the  yoke  and  armature,  should  form  as  nearly  as 
possible  a  closed  magnetic  circuit.  The  cross-sections 
of  yokes  should  be  as  great  as  those  of  the  cores. 

Many  special  forms  1  of  electromagnet  have  been  devised 
for  special  purposes.  A  special  form  of  electromagnet  de- 
vised by  Ruhmkorff 
for  experiments  on  di- 
amagnetism  is  shown 
in  Fig.  207.  A  still 
more  powerful  form, 
designed  to  produce 
exceedingly  intense 
magnetic  fields  in  the 
space  between  its 
poles,  is  the  half-ring 
electromagnet  de- 
signed by  H.  Du  Bois, 
Fig.  217.  It  consists 
of  two  iron  quadrants, 
circular  in  section, 
which  are  bolted  to  a  massive  iron  yoke  forming  the  base  of 
the  electromagnet.  The  pole  faces  are  very  close  together 
and  are  reduced  to  a  smaller  diameter  than  the  main  limbs 
so  as  to  obtain  a  highly  concentrated  and  uniform  mag- 
netic field.  The  coils  are  in  sections  which  enable  various 
degrees  of  magnetization  to  be  obtained.  To  give  a  very 
powerful  holding-on  action,  a  short  cylindrical  electromagnet 
surrounded  by  an  outer  iron  tube,  united  at  the  bottom  by 
iron  to  the  iron  core,  is  found  best ;  the  iron  jacket  constitut- 

1  For  descriptions  of  these,  as  well  as  for  discussion  of  all  other  matters 
relating  to  the  subject,  see  the  author's  treatise  on  The  Electromagnet  and 
Electromagnetic  Mechanism. 


impiiiiiiiiiiii 
FIG.  216.  —  A  Laboratory  Electromagnet. 


380 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  414 


ing  a  return  path  for  the  magnetic  lines.  This  form  is  known 
as  an  iron-clad  magnet.  To  attract  iron  across  a  wide  gap 
which  offers  much  reluctance,  a  horse-shoe  shape  with  long 
cores  should  be  chosen ;  for  it  needs  long  cores  on  which  to 
wind  wire  enough  to  provide  sufficient  excitation  to  drive 
the  flux  across  the  gap.  To  give  a  gentle  pull  over  a  long 
range  a  long  tubular  coil  (Art.  416),  having  a  long  movable 

iron  core  is  used. 
For  very  quick-act- 
ing magnets  the  coils 
should  not  be  wound 
all  along  the  iron, 
but  only  round  the 
poles,  and  they 
should  be  small. 

414.  Solenoid.  — 
Without  any  cen- 
tral core  of  iron  or 
steel  a  spiral  coil 
of  wire  traversed  by 
a  current  acts  as 
an  electromagnet 
(though  not  so  powerfully  as  when  an  iron  core  is  placed  in 
it).  Such  a  coil  is  sometimes  termed  a  solenoid.  A  solenoid 
has  two  poles  and  a  neutral  equatorial  region.  Ampere 
found  that  it  will  attract  magnets  and  be  attracted  by  mag- 
nets. It  will  attract  another  solenoid;  it  has  a  magnetic 
field  resembling  generally  that  of  a  bar  magnet.  If  so 
arranged  that  it  can  turn  round  a  vertical  axis,  it  will  set 
itself  in  a  North  and  South  direction  along  the  magnetic 
meridian.  Fig.  218  shows  a  solenoid  arranged  with  pivots, 
by  which  it  can  be  suspended  to  a  "  table,"  like  that  shown  in 
Fig.  227. 

With  an  iron  core  the  solenoid  becomes  far  more  powerful. 
The  effect  of  the  iron  core  is,  by  its  greater  permeability,  to 
multiply  the  number  of  magnetic  lines  as  well  as  to  con- 


FIG.  217.  —  Half-ring  Electromagnet  of  Du  Bois. 


CH.  v.  414] 


SOLENOID 


381 


centrate  them  at  definite  poles.  The  student  has  been  told 
(Art.  215)  that  the  lines  of  force  due  to  a  current  flowing  in 
a  wire  are  closed  curves,  approximately  circles  (Figs.  127, 
193,  and  223),  round  the  wire.  If  there  were  no  iron  core 
many  of  these  little  circular  lines  of  force  would  simply  re- 
main as  small  closed  curves  around  their  own  wire  ;  but,  since 
iron  has  a  permeability  hundreds  of  times  greater  than  air, 
wherever  the  wire  passes  near  an  iron  core  the  magnetic 
lines  alter  their  shape,  and  _^ 

instead  of  being  little  circles 
around  the  separate  wires, 
run  through  the  iron  core 
from  end  to  end,  and  round 
outside  from  one  end  of  the 
coil  back  to  the  other.  A 
few  of  the  magnetic  lines  do 

this  when  there  is  no  iron  ;  almost  all  of  them  do  this  when 
there  is  an  iron  core  ;  and  when  there  is  an  iron  core  there  are 
many  more  lines  to  flow  back.1  Hence  the  electromagnet 
with  its  iron  core  has  enormously  stronger  poles  than  the 
spiral  coil  or  solenoid  would  have  alone. 

In  Art.  369  it  was  shown  that  the  intensity  of  the  magnetic 
field  down  the  middle  of  a  solenoid  of  length  Z,  having  S 
spirals,  carrying  i  amperes,  is  — 


10 


Since  the  area  enclosed  is  irr2,  the  flux  down  the  long  tubu- 
lar solenoid  (without  iron)  will  be 


1  But  in  the  case  of  a  permanent  steel  horse-shoe  magnet,  bringing  up 
the  iron  keeper,  though  it  concentrates  the  lines  through  the  poles,  does 
not  increase  the  total  number  of  lines  through  the  bend  of  the  U.  Compare 
Figs.  91  a,  b,  and  c,  p.  126,  with  Figs.  210  a,  b,  and  c,  p.  374. 


382  ELECTRICITY  AND   MAGNETISM      [PT.  n.  415 

And,  since  4?r  magnetic  lines  go  to  one  unit  of  magnetism, 
the  solenoid  (without  iron)  will  act  (if  there  is  no  leakage) 
as  though  it  had  at  its  pole  the  magnetism  — 


It  will  be  noticed  that  for  any  solenoid  of  given  length 
and  radius  the  three  magnetic  quantities  §  (internal  field), 
g  (magnetic  flux),  and  m  (strength  of  poles)  are  proportional 
to  the  amperes  of  current  and  to  the  number  of  turns  in  the 
coil,  that  is  to  say,  to  the  ampere-turns. 

415.  Lifting-power  of  Electromagnets.  —  The  force  with 
which  an  electromagnet  holds  on  to  its  armature  depends 
not  only  on  its  magnetic  strength,  but  also  upon  its  form, 
and  on  the  shape  of  its  poles,  and  on  the  form  of  the  soft 
iron  armature  which  it  attracts.  It  should  be  so  arranged 
that  as  many  lines  of  force  as  possible  should  run  through 
the  armature,  and  the  armature  itself  should  contain  a  suffi- 
cient mass  of  iron.  Joule  designed  a  powerful  electromagnet, 
capable  of  supporting  over  a  ton.  The  maximum  pull  he 
could  produce  between  an  electromagnet  and  its  armature 
was  200  Ibs.  per  square  inch,  or  about  13,800,000  dynes  per 
square  centimetre.  Bidwell  found  the  attraction  to  go  up 
to  226-3  Ibs.  per  square  inch  when  the  wrought-iron  core 
was  saturated  up  to  19,820  magnetic  lines  to  the  square 
centimetre.  The  law  of  traction  is  that  the  pull  per  square 
centimetre  is  proportional  to  the  square  of  the  number  of 
lines  per  square  centimetre  :  or,  in  symbols, 


where/  is  the  pull  in  dynes,  and  A  the  area  in  square  centims. 
In  the  following  table  are  given  the  values  of  the  tractive 
force  for  different  degrees  of  magnetization. 


CH.  v.  416]          PLUNGER  ELECTROMAGNET 


383 


93 
LINES  PER  SQ.  CM. 

DYNES  PER  SQ. 
CENTIM. 

GRAMMES  PER 
SQ.  CENTIM. 

POUNDS  PER 
SQ.  INCH 

1,000 

39,790 

40-56 

G'577 

2,000 

159,200 

162'3 

2'308 

3,000 

358,100 

365-1 

5-190 

4,000 

636,600 

648-9 

9*228 

5,000 

994,700 

1,014 

14-39 

6,000 

1,432,000 

1,460 

20-75 

7,000 

1,950,000 

1,987 

28-26 

8,000 

2,547,000 

2,596 

36*95 

9,000 

3,223,000 

3,286 

46-72 

10,000 

3,979,000 

4,056 

57-68 

12,000 

5,730,000 

5,841 

83-07 

14,000 

7,800,000 

7,950 

113-1 

16,000 

10,170,000 

10,390 

147*7 

18,000 

12,890,000 

13,140 

186-8 

20,000 

15,920,000 

16,230 

230-8 

It  will  be  noted  that  doubling  33  makes  the  pull  four 
times  as  great.  One  curious  consequence  of  this  law  is 
that  to  enlarge  its  poles  weakens  the  pull  of  an  electromagnet 
or  magnet.  In  some  cases  —  bar  magnets  for  example  — 
their  tractive  power  is  increased  by  bevelling  down  or  round- 
ing the  poles  so  as  to  concentrate  33. 

416.  Plunger  Electromagnet.  —  A  solenoid  with  a  movable 
iron  plunger  is  sometimes  called  a  plunger  electromagnet,  or  a 
sucking-magnet.  The  iron  core  tends  to  move  into  the 
position  in  which  it  best  completes  (Art.  409)  the  magnetic 
circuit.  If  the  core  is  much  longer  than  the  tubular  coil, 
the  pull  increases  as  the  end  of  the  core  penetrates  down  the 
coil,  being  a  maximum  when  the  end  of  the  iron  rod  has 
about  reached  the  end  of  the  tube.  Short  iron  cores  are  only 
pulled  while  at  the  mouth  of  the  coil;  the  maximum  pull 
being  when  about  half  their  length  has  entered. 

Fig.  219  depicts  a  form  of  plunger  electromagnet  in  very 
extensive  use.  The  soft  iron  plunger,  which  is  usually  coned 
at  the  end,  is  pulled  up,  when  the  exciting  current  is  switched 
on,  inside  a  heavy  coil  of  insulated  wire  wound  on  a  brass 


384 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  417 


tube.  To  increase  the  pull  a  short  fixed  core  of  iron  is  in- 
serted at  the  top ;  and  an  iron  jacket  or  external  frame 
provides  a  good  return  path  for  the  magnetic  flux.  Such  a 
magnet  may  be  designed  to  exert  a  pull  of  100  Ibs.  or  more, 
with  a  range  of  travel  of  2  or  3  inches.  In  this  case  also  the 
core  tends  so  to  move  as  to  close  up  the  gap  in  the  magnetic 
circuit,1  and  to  make  the  product  of  the  flux 
and  the  ampere-turns  with  which  it  is  inter- 
linked a  maximum  (Art.  409). 

417.  The  Winding  of  Electromagnets.  - 
The  exact  laws  governing  the  winding  of 
electromagnets  are  somewhat  complicated ; 
but  it  is  easy  to  give  certain  rules  which  are 
approximately  true.  Every  electromagnet 
shows  the  same  general  set  of  facts  —  that 
with  small  exciting  power  there  is  little 
magnetism  produced,  with  larger  exciting 
power  there  is  more  magnetism,  and  that 
with  very  great  exciting  power  the  iron  be- 
comes practically  saturated  and  will  take 
up  very  little  additional  magnetism.  It  follows  at  once  that 
if  the  electromagnet  is  destined  to  be  used  at  the  end  of  a  long 
line  through  which  only  a  small  current  (perhaps  only  y^  am- 
pere will  flow,  the  requisite  number  of  ampere-turns  to  excite 
the  magnetism  will  not  be  attained  unless  some  thousands 
of  turns  of  wire  are  used ;  and  as  the  current  is  small  a  fine 
wire  may  be  used. 

It  may  be  noted  that  when  electromagnets  are  wound 
with  many  turns  of  fine  wire,  these  coils  will  add  to  the 
electric  resistance  of  the  circuit,  and  will  tend  to  diminish 
the  current.  Herein  lies  a  difference  in  construction  of  tele- 

1  The  following  is  the  law  expressing  the  pull,  in  dynes,  of  a  plunger 
magnet :  — 


FIG.  219.  —  Plunger 
Electromagnet. 


wherein  dP  stands  for  the  change  in  the  permeance  (Art.  404)  due  to  a 
forward  travel  of  the  plunger  through  dx  centimetres. 


CH.  v.  417]        WINDING   OF   ELECTROMAGNETS  385 

graphic  and  other  instruments ;  for  while  electromagnets 
with  "  long  coils,"  consisting  of  many  turns  of  fine  wire, 
must  be  used  on  long  circuits  where  there  is  great  line  re- 
sistance, such  an  instrument  would  be  of  no  service  in  a 
laboratory  circuit  of  very  small  resistance,  for  the  resistance 
of  a  long  thin  coil  would  be  disproportionately  great :  here 
a  short  coil  of  few  turns  of  stout  wire  would  be  appropriate 
(see  Art.  207). 

It  is  the  nature  of  the  line,  according  to  whether  it  is  of 
high  resistance  or  low,  which  governs  the  questions  how  the 
coil  shall  be  wound  and  how  the  battery  shall  be  grouped. 

Similar  electromagnets  of  different  sizes  must  have  ampere- 
turns  proportional  to  their  linear  dimensions  if  they  are  to 
be  raised  to  equal  degree  of  saturation. 

As  the  magnetism  of  the  magnet  depends  on  the  number 
of  ampere-turns,  it  should  make  no  matter  whether  the  coils 
are  bigger  than  the  core  or  whether  they  enwrap  it  quite 
closely.  If  there  were  no  magnetic  leakage  this  would  be 
true  in  one  sense;  but  for  an  equal  number  of  turns  large 
coils  cost  more  and  offer  higher  resistance.  Hence  the  coils 
are  wound  as  closely  to  the  iron  core  as  is  consistent  with 
good  insulation.  Also  the  iron  is  chosen  as  thick  as  possible, 
as  permeable  as  possible,  and  forming  as  compact  a  magnetic 
circuit  as  possible,  so  that  the  magnetic  resistance  may  be 
reduced  to  its  utmost,  giving  the  greatest  amount  of  mag- 
netism for  the  number  of  ampere-turns  to  excitation.  This 
is  why  horse-shoe-shaped  electromagnets  are  more  powerful 
than  straight  electromagnets  of  equal  weight ;  and  why  also 
a  horse-shoe  electromagnet  will  only  lift  about  a  quarter  as 
much  load  if  one  pole  only  is  used  instead  of  both. 

As  the  coils  of  electromagnets  grow  hot  with  the  current, 
sufficient  cooling  surface  must  be  allowed,  or  they  may  char 
their  insulation.  Each  square  centimetre  of  surface  warmed 
1°  C.  above  the  surrounding  air  can  get  rid  of  about  0-0029 
watt.  If  50°  above  the  surrounding  air  be  taken  as  the  safe 
limit  of  rise  of  temperature,  and  the  electromagnet  has 
2c 


386         ELECTRICITY   AND   MAGNETISM    [PT.  n.  418,  419 

resistance  r  and  surface  s  sq.  cms.,  the  highest  permissible 
current  will  be  0-38  Vs/r  amperes. 

Where  the  coils  of  electromagnets  are  to  be  excited  from 
circuits  at  a  given  voltage,  the  excitation  (i.e.  ampere-turns) 
which  they  receive  depends  on  the  mean  resistance  of  one 
turn  of  the  coil,  and  is  practically  independent  of  the  num- 
ber of  coils.  For,  supposing  the  mean  resistance  per  turn  to 
remain  the  same,  doubling  the  number  of  turns  will  double 
the  resistance,  and  will  therefore  halve  the  current.  But  if 
half  the  current  goes  twice  as  many  times  round,  the  ampere- 
turns  will  be  unchanged.  By  this  argument,  the  excitation 
should  also  remain  unchanged  if  half  the  coils  were  removed  ; 
and  indeed  this  would  be  true  if  the  remaining  coils  did  not 
overheat. 

418.  Polarized   Mechanism.  —  An  electromagnet  moves 
its  armature  one  way,  no  matter  which  way  the  current 
flows.     Reversing  the  current  makes  no  difference.     There 
are,  however,  two  means  of  designing  a  mechanism  that  will 
cause  an  armature  to  move  in  either  sense  at  will,     (a)  The 
armature's  movement  is  controlled  by  an  adjusted  spring 
so  as  to  be  in  an  intermediate  position  when  a  weak  current 
is  flowing.     Then  sending  a  stronger  current  will  move  the 
armature  one  way,  and  weakening  or  stopping  the  current 
will  make  it  move  the  other  way.     (6)  A  polarized  armature 
or  tongue  (i.e.  one  that  is  independently  magnetized)  is  placed 
between  the  poles  of  the  electromagnet  instead  of  opposite  them. 
The  direction  in  which  it  tends  to  move  will  be  reversed  by 
reversing  the  current  in  the  circuit  of  the  electromagnet. 

419.  Growth  of  Magnetism.  —  It  requires  time  to  mag- 
netize an  iron  core.     This  is  mainly  due  to  the  fact  that  a 
current,  when  first  switched  on,  does  not  instantly  attain 
its  full  strength,  being  retarded  by  the  self-induced  counter- 
electromotive-force  (Art.  501) ;    it  is  partly  due  to  the  re- 
action of  transient  eddy-currents  (Art.  500)  induced  in  the 
iron  itself.     Faraday's  large  electromagnet  at  the   Royal 
Institution  takes  about  two  seconds  to  attain  its  maximum 


CH.  v.  420]    MAGNETIC   FIELDS  AND   CURRENTS         387 

strength.  The  electromagnets  of  large  dynamo  machines 
often  take  ten  minutes  or  more  to  rise  to  their  working  stage 
of  magnetization. 

When  electromagnets  are  used  with  rapidly-alternating 
currents  (Art.  522)  there  are  various  different  phenomena, 
for  which  the  student  is  referred  to  Art.  533. 


LESSON  XXXII.  —  Electrodynamics 

420.  Electrodynamics.  —  In  1821,  almost  immediately 
after  Oersted's  discovery  of  the  action  of  a  current  on  a 
magnet,  Ampere  discovered  that  a  current  acts  upon  another 
current,  apparently  attracting  it 1  or  repelling  it  according 
to  certain  definite  laws.  These  actions  he  investigated  by 


FIG.  220.  —  Field  due  to  two  Currents  in  the  same  direction. 

experiment,  and  from  the  experiments  he  built  up  a  theory 
of  the  force  exerted  by  one  current  on  another.  That  part 
of  the  science  which  is  concerned  with  the  force  which  one 
current  exerts  upon  another  he  termed  Electrodynamics. 
It>  is  now  known  that  these  actions  are  purely  magnetic,  and 
are  due  to  stresses  in  the  intervening  medium.  The  mag- 
netic field  around  a  single  conductor  consists  of  a  magnetic 
whirl  (Arts.  215  and  370),  and  any  other  conductor  carrying 

1  It  would  be  more  correct  to  speak  of  these  (mechanical)  forces  as  acting 
on  the  conductors  carrying  currents,  than  as  acting  on  the  currents  themselves. 


388 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  421 


a  current  when  brought  into  the  field  of  the  first  is  acted 
upon  by  it.  We  may  determine  graphically  the  form  of  the 
magnetic  field  surrounding  two  parallel  conductors  carrying 


FIG.  221.  —  Field  due  to  two  Currents  in  opposite  directions. 

currents  by  applying  the  principle  of  superposition  (Art.  144) 
as  in  Figs.  220  and  221,  which  may  be  compared  with  Figs. 
222  and  223,  obtained  when  the  two  conductors  were  passed 
through  holes  in  a  sheet  of  glass  on  which  iron  filings  were 
sprinkled.  In  Figs.  220  and  222  the  currents  flow  in  the 
same  direction ;  in  Figs.  221  and  223,  in  opposite  directions. 


FIG.  222.  —  Filing  Figure  of 
Concurrent  Currents. 


FIG.  223.  —  Filing  Figure  of 
Opposed  Currents. 


In  the  first  case  the  stresses  in  the  field  (Art.  121)  tend  to 
pull  them  together,  in  the  second  to  push  them  apart.1 

421.    Laws  of  Parallel  and  Oblique  Circuits.  —  The  fol- 
lowing are  the  laws  discovered  by  Ampere  :  — 

1  See  article  by  the  author  in  the  Philosophical  Magazine,  November 
1878,  p.  348. 


CH.  v.  421]          ATTRACTION   OF   CURRENTS  389 

(i.)  Two  parallel  portions  of  a  circuit  attract  one  another  if 
the  currents  in  them  are  flowing  in  the  same  direction,  and  repel 
one  another  if  the  currents  flow  in  opposite  directions. 

This  law  is  true  whether  the  parallel  wires  be  parts  of  two 
different  circuits  or  parts  of  the  same  circuit.  The 
separate  turns  of  a  spiral  coil,  like  Fig.  218,  when 
traversed  by  a  current  attract  one  another;  such  a 
coil,  therefore,  shortens l  when  a  current  is  sent 
through  it.  But  this  is  equally  well  explained  by  the 
general  law  of  electromagnetic  systems  (Art.  409), 
because  shortening  will  re- 
duce the  reluctance  of  the  "^  ..^-^.n. 
magnetic  circuit  and  in-  FlG-  224'  ~  B™fes°f  Thin  FIexible 
crease  the  interlinkage  of 

the  flux  with  the  electric  current.  If  into  a  circuit  a 
number  of  thin  flexible  wires  in  parallel  with  one  an- 
other (Fig.  224)  are  introduced,  then  on  switching  on 
the  current  they  will  tend  to  close  up  together. 

(ii.)  Two  portions  of  circuits  crossing  one  another  obliquely 
attract  one  another  if  both  the  currents  run  either  towards  or 

from  the  point  of  crossing, 
and  repel  one  another  if  one 
runs  to  and  the  other  from 
that  point. 

Fig.  225  gives  three 
cases  of  attraction 
and  two  of  repul- 

1         i. •  sion  that  occur  in 

these  laws. 

FIG.  225. -Cases  ^Opposing  and  Concurrent  (^    w^    an    demeni 

,  of  a  circuit  exerts  a  force 

on  another  element  of  a  circuit,  that  force  always  tends  to  urge 
the  latter  in  a  direction  at  right  angles  to  its  own  direction.    Thus, 

1  This  is  the  mode  of  operation  of  Roget's  dancing  spiral,  an  open  coil 
of  wire  fixed  at  the  top,  and  the  lower  end  of  which  dips  into  a  mercury  cup. 


390  ELECTRICITY   AND   MAGNETISM      [PT.  n.  422 

in  the  case  of  two  parallel  circuits,  the  force  of  attraction  or 
repulsion  acts  at  right  angles  to  the  currents  themselves. 

An  example  of  laws  ii.  and  iii.  is  afforded  by  the  case 
shown  in  Fig.  226.  Here  two  currents  ab  and  cd  are 
movable  round  O  as  a  centre. 
There  will  be  an  apparent  re- 
pulsion between  a  and  d  and 
between  c  and  b,  while  in  the 
other  quadrants  there  will  be 
an  apparent  attraction,  a  at-  FIG.  226.  —  Mutual  Action  of 
tracting  c,  and  b  attracting  d. 

The  foregoing  laws  may  be  summed  up  in  one,  by  saying 
that  two  portions  of  circuits,  however  situated,  set 
up  stresses  in  the  surrounding  medium  tending  to  set 
them  so  that  their  currents  flow  as  nearly  in  the  same 
path  as  possible. 

(iv.)  The  force  exerted  between  two  parallel  portions  of  cir- 
cuits is  proportional  to  the  product  of  the  strengths  of  the  two 

currents,  to  the  length  of 
the  portions,  and  in- 
versely proportional  to  the 
simple  distance  between 
them. 

422.  Ampere's  Table. 
—  In  order  to  observe 
these  attractions  and 
repulsions,  Ampere  de- 
vised the  piece  of  ap- 
paratus known  as  Am- 
pere's Table,  shown  in 

FIG.  227.  —  Ampere's  Table. 

Fig.   227,   consisting  of 

a  double  supporting  stand,  upon  which  wires,  shaped  in 
different  ways,  can  be  so  hung t as  to  be  capable  of  rotation. 
The  ends  of  the  suspended  wires  dip  into  two  mercury  cups, 
so  as  to  ensure  good  contact,  while  allowing  freedom  to  move. 


CH.  v.  423]  AMPERE'S   THEORY  391 

By  the  aid  of  this  piece  of  apparatus  Ampere  further 
demonstrated  the  following  points  :  — 

(a)  A  circuit  doubled  back  upon  itself,  so  that  the  current  flows 
back  along  a  path  close  to  itself,  exerts  no  force  upon  ex- 
ternal points. 

(6)  A  circuit  bent  into  zigzags  or  sinuosities  produces  the 
same  magnetic  effects  on  a  neighbouring  piece  of  circuit  as 
if  it  were  straight. 

(c)  There  is  in  no  case  any  force  tending  to  move  a  conductor 

in  the  direction  of  its  own  length. 

(d)  The  force  between  two  conductors  of  any  form  is  the  same 
whatever  the  linear  size  of  the  system,  provided  the  dis- 
tances be  increased  in  the  same  proportion,  and  that  the 
currents  remain  the  same  in  strength. 

The  particular  case  given  in  Fig.  228,  will  show  the  value  of 
these  experiments.  Let  AB  and  CD  represent  two  wires  carrying 
currents,  lying  neither 
parallel  nor  in  the  same 

plane.     It  follows  from  /  \  g  ^<^Q 

(6)   that   if   we   replace  /  /    ,^^5'^^^^>B 

the  portion  PQ  by  the 
crooked  wire  PRSQ, 
the  force  will  remain  the 
same.  The  portion  PR 
is  drawn  vertically  down-  /  P* 

wards,  and  as  it  can,  by 

FIG.  228.  —  Forces  between  Oblique  Conductors. 

(c),  experience  no  force 

in  the  direction  of  its  length,  this  portion  will  neither  be  attracted 
nor  repelled  by  CD.  In  the  portion  RS  the  current  runs  at  right 
angles  to  CD,  and  this  portion  is  neither  attracted  nor  repelled  by 
CD.  In  the  portion  SQ  the  current  runs  parallel  to  CD,  and  in 
the  same  direction,  and  will  therefore  be  attracted  downwards. 
On  the  whole,  therefore,  PQ  will  be  urged  towards  CD.  The 
portions  PR  and  RS  will  experience  forces  of  rotation,  however,  P 
being  urged  round  R  as  a  centre  towards  C,  and  R  being  urged 
horizontally  round  S  towards  C.  These  actions  would  tend  to 
make  AB  parallel  with  CD. 

423.  Ampere's  Theory.  —  From  the  four  preceding  ex- 
perimental data,  Ampere  built  up  an  elaborate  mathematical 
theory,  assuming  that,  in  the  case  of  these  forces  acting 


/ 


392 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  423 


apparently  at  a  distance  across  empty  space,  the  action  took 
place  in  straight  lines  between  two  points,  the  total  attrac- 
tion being  calculated  as  the  sum  of  the  separate  attractions 
on  all  the  different  parts. 

The  briefest  summary  must  suffice.  If  we  deal  first  with  two 
parallel  elements  of  length  dli  and  dl2  carrying  currents  2^2,  and 
set  at  right  angles  to  the  distance  r  joining  them,  their  mutual 
forqe  will  be 

df  =   -  ifadldk  100  r2. 


If,  however,  they  are  not  parallel  or  in  one  plane,  let  <t>  be  the 
angle  they  make  with  one  another,  while  0i  and  02  are  the  angles 
they  make  with  r  ;  when 


df  =   - 


(cos  0  —  f  cos  0i.  cos  02)/100r2. 


By  integrating  this  expression  one  obtains  the  forces  for  circuits 
of  any  given  dimensions.  For  example,  for  two  parallel  straight 
conductors  of  lengths  W2,  if  these  lengths  are  great  compared  with 
the  distance  r  between  them,  we  have 


r2. 

The  researches  of  Faraday  have,  however,  led  to  other 
views  ;  the  mutual  attractions  and  repulsions  being  regarded 

as  due  to  actions  tak- 
ing place  in  the  me- 
dium which  fills  the 
space  around  and  be- 
tween the  conductors. 
All  these  so-called 
electrodynamic  ac- 
tions are  merely  mag- 
netic actions. 

An  interesting  experiment,  showing  an  apparent  mutual 
self-repulsion  between  contiguous  portions  of  the  circuit, 
was  devised  by  Ampere.  A  trough  divided  by  a  partition 
into  two  parts,  and  made  of  non-conducting  materials,  is 
filled  with  mercury.  Upon  it  floats  a  metallic  bridge  formed 


FIG.  229.  —  Apparent  Repulsion  between  Contiguous 
Parts  of  a  Circuit. 


CH.  v.  424,  425]      ELECTRODYNAMOMETER 


393 


of  a  bent  wire,  of  the  form  shown  in  Fig.  229,  or  consisting 
of  a  glass  tube  filled  siphonwise  with  mercury.  When  a 
current  is  sent  through  the  floating  conductor  from  X  over 
MN,  and  out  at  Y,  the  floating  bridge  is  observed  to  move 
so  as  to  increase  the  area,  and  therefore  the  magnetic  flux, 
enclosed  by  the  circuit.  But  the  force  would  be  diminished 
indefinitely  if  the  two  parallel  parts  could  be  made  to  lie 
quite  close  to  one  another. 

424.  Pinch  Effect.  —  The  whirls  of  magnetic  field  that 
surround  (Art.  370)  the  conductor  carrying  the  current  tend 
to  contract,  producing  resultant   inward  radial  forces.     If 
the  conductor  is  a  liquid, 

such  as  mercury  or  molten 
metal  in  a  channel,  these 
external  forces  tend  to 
squeeze  the  liquid  into  a 
lesser  cross-section.  The 
pressure  is  proportional 
to  the  square  of  the  cur- 
rent and  inversely  propor- 
tional to  the  cross-section. 
Hence,  if  at  any  place  the 
channel  is  contracted,  the 
forces  tending  to  pinch 
the  conductor  are  greater 
than  at  the  wider  places, 
causing  liquid  to  move 
away  from  the  pinched 
place,  which  therefore  is  still  further  reduced  in  section,  and 
actually  parts  in  two.  This  is  known  as  the  pinch  effect.  It 
is  a  mechanical  effect  due  to  the  self-induced  magnetic  field 
of  the  current. 

425.  Electrodynamometer.  —  Weber    devised    an   instru- 
ment known  as   an  electrodynamometer  for  measuring  the 
strength  of  currents  by  means  of  the  electrodynamic  action 
of  one  part  of  the  circuit  upon  another  part.     It  is  a  sort  of 


FIG.  230.  —  Electrodynamometer,  with  Bifilar 
Suspension. 


394  ELECTRICITY   AND   MAGNETISM         [FT.  n.  426 

galvanometer,  in  which,  instead  of  a  needle,  there  is  a  small 
coil  suspended.  One  form  of  this  instrument,  in  which 
both  the  large  outer  and  small  inner  coils  consist  of  two 
parallel  coils  of  many  turns,  is  shown  in  Fig.  230.  The 
inner  coil  CD  is  suspended  with  its  axis  at  right  angles  to 
that  of  the  outer  coils  A  A,  BB,  and  is  supported  bifilarly 
(see  Art.  132)  by  two  fine  metal  wires.  If  one  current 
flows  round  both  coils  in  either  direction  the  inner  bobbin 
tends  to  turn  and  set  its  coils  parallel  to  the  outer  coils ;  the 
sine  of  the  angle  through  which  the  suspending  wires  are 
twisted  being  proportional  to  the  square  of  the  strength  of 
the  current. 

If  G  be  the  "  principal  constant  "  (Art.  226)  of  the  large  coils, 
and  g  the  "  moment  "  of  the  small  coils  (Art.  373)  when  carrying 
unit  current,  and  ifa  the  currents  in  them,  the  torque  or  turning 
moment  will  be  (in  dyne-centimetres), 

T  =  G0iii2/100. 

The  chief  advantage  of  this  instrument  over  a  galva- 
nometer is,  that  it  may  be  used  for  alternating  currents ;  a 
current  in  one  direction  being  followed  by 
a  reverse  current,  perhaps  thousands  of 
times  in  a  minute.  Such  currents  hardly 
affect  a  galvanometer  needle  at  all;  the 
needle  simply  quivers  in  its  place  without 
turning. 

426.  Siemens's  Electrodynamometer.  - 
In  Siemens's  dynamometer  (Fig.  231),  much 
used  for  measurement  of  strong  currents, 
whether  of  the  continuous  or  the  alternat- 
™&  kind> one  coil  is  fixed  permanently,  whilst 
the  other  coil,  of  one  or  two  turns,  dipping 
with  its  ends  in  mercury  cups,  is  hung  at  right  angles,  and 
controlled  by  a  spiral  spring  below  a  torsion-head.  When 
current  passes,  the  movable  coil  tends  to  turn  parallel  to  the 
fixed  coils,  but  is  prevented ;  the  torsion  index  being  turned 


CH.  v.  427] 


CURRENT   BALANCES 


395 


FIG.  232.  —  Principle  of  the  Kelvin  Current  Balance. 


until  the  twist  on  the  spring  balances  the  torque.  The  angle 
through  which  the  index  has  had  to  be  turned  is  proportional 
to  the  product  of  iiiz,  the  currents  in  the  fixed  and  movable 
coils. 

For  use  of  dynamometer  as  wattmeter,  see  Art.  458. 

427.  Kelvin's  Current  Balances.  —  Joule,  Mascart,  Lord 
Rayleigh,  and  others  have  measured  currents  by  balances 
in  which  gravity  was  opposed  to  the  attraction  or  repulsion 
of  two  coils.  Of  such  balances  the  most  perfect  are  those 
of  Lord  Kelvin, 

the  principle  of  m^-,  ^  \  ^  „.  /  C  6^=>  }C 
which  is  outlined 
in  Fig.  232.  There 
are  four  fixed 
coils,  ABCD,  be- 
tween which  is 
suspended,  by  a 

flexible  metal  ligament  of  fine  wires,  at  the  ends  of  a  light 
beam,  a  pair  of  movable  coils,  E  and  F.  The  current  flows 
in  such  directions  through  the  whole  six  that  the  beam  tends 
to  rise  at  F  and  sink  at  E.  The  beam  carries  a  small  pan  at 
the  F  end,  and  a  light  arm,  not  shown  in  Fig.  232,  but  shown 
in  Fig.  233,  along  which,  as  on  a  steel-yard,  a  sliding  weight 
can  be  moved  to  balance  the  torque  due  to  the  current. 
The  current  is  proportional  to  the  square-root  of  this  torque, 
since  the  force  is  proportional  to  the  product  of  the  current 
in  the  fixed  and  movable  coils  as  in  all  electrodynamometers. 

Lord  Kelvin  designed  a  whole  range x  of  these  instruments : 
—  a  centi-ampere  balance  reading  from  0*01  to  1  ampere ;  a  deci- 
ampere  balance  reading  from  O'l  to  10;  a  deka-ampere  balance 
reading  from  1  to  100 ;  a  hekto-ampere  balance  reading  from  6  to 
600 ;  and  a  kilo-ampere  balance  reading  up  to  2500  amperes.  In 
the  centi-ampere  balance,  shown  in  Fig.  233,  the  sliding  weight  is 
carried  on  the  base  of  the  pointer  (shown  white),  and  when  at  the 

1  For  a  fuller  account  of  these  Current  Balances,  and  of  the  Wattmeters 
on  the  same  principle,  see  Gray's  Absolute  Measurements  in  Electricity  and 
Magnetism,  from  which  Fig.  233  is  taken. 


396 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  427 


zero  of  the  scale  just  balances  the  weight  in  the  V-shaped  pan.  Any 
current  passing  through  the  coils  causes  the  beam  to  tilt  and  the 
pointer  is  moved  (by  means  of  a  self-releasing  slider  attached  to 


cords)  until  it  is  again  horizontal  (as  shown  by  the  black  pointer  at 
either  end).  With  a  certain  pair  of  weights  the  fixed  scale  gives  the 
current  in  decimal  parts  of  an  ampere;  but  by  the  use  of  other 
weights  a  wider  range  is  obtained. 


CH.  v.  428]      ELECTROMAGNETIC   ROTATIONS 


397 


The  "  ampere-standard "  instrument,  and  the  "  volt- 
standard  "  instruments  of  the  Board  of  Trade,  kept  at 
Whitehall  as  legal  standards  for  Great  Britain,  are  current 
balances  of  special  construction,  designed  by  the  late  Major 
Cardew. 

428.  Electromagnetic  Rotations.  —  Continuous  rotation 
can  be  produced  between  a  magnet  and  a  circuit,  or  between 
two  parts  of  one  circuit,  provided  that  one 
part  of  the  circuit  can  move  while  another 
part  remains  fixed,  or  that  the  current  in 
one  part  can  be  reversed.  The  latter  de- 
vice is  adopted  in  the  construction  of  elec- 
tric motors  (Art.  516).  The  former  alterna- 
tive is  applied  in  some  historic  apparatus 
for  showing  rotations,  a  sliding-contact 
being  made  between  one  part  of  the  circuit 
and  another.  The  earliest  form  of  rotation- 
apparatus  was  devised  by  Faraday  in  1822. 
It  is  shown  in  Fig.  234,  in  which  a  wire 
carrying  a  current  is  jointed  at  the  top  and 
dips  into  a  cup  of  mercury  surrounding  the 
pole  of  a  magnet.  On  switching  on  the 
current  the  wire  at  once  begins  to  walk  round  the  pole  with 
a  motion  that  continues  until  the  current  is  switched  off. 

A  pole  of  a  magnet  can  also  be  made  to  rotate  round  a 
current;  and  if  a  vertical  magnet  be  pivoted  so  as  to  turn 
around  its  own  axis  it  will  rotate  when  a  current  is  led  into 
its  middle  region  and  out  at  either  end.  If  the  current  is 
led  in  at  one  end  and  out  at  the  other  there  will  be  no  rota- 
tion, since  the  two  poles  would  thus  be  urged  to  rotate  in 
opposite  ways.  Liquid  conductors  too  can  exhibit  electro- 
magnetic rotations.  Let  a  cylindrical  metallic  vessel  con- 
nected to  one  pole  of  a  battery  be  filled  with  mercury  or 
dilute  acid,  and  let  a  wire  from  the  other  pole  dip  into  its 
middle,  so  that  a  current  may  flow  radially  from  the  centre 
to  the  circumference,  or  vice  versa;  then,  if  this  be  placed 


FIG.  234.  —  Faraday's 
Apparatus  for  Elec- 
tromagnetic '  Rota- 
tions. 


398  ELECTRICITY   AND   MAGNETISM     [PT.  n.  429 

upon  the  pole  of  a  powerful  magnet,  or  if  a  magnet  be  held 
vertically  over  it,  the  liquid  may  be  seen  to  rotate. 

429.  Electromagnetic  Actions  of  Convection  Currents. — 
According  to  Faraday  a  stream  of  particles  charged  with 
electricity  acts  magnetically  like  a  true  conduction  current. 
This  was  first  proved  in  1876  by  Rowland,  who  found  a 
rapidly  rotated  charged  disk  to  act  upon  a  magnet  as  a 
feeble  circular  current  would  do.  If  a  number  of  charges, 
each  of  equal  value,  follow  one  another,  so  that  there  are 
q  units  per  centimetre  along  the  procession,  and  the  procession 
travels  with  a  velocity  of  v  centimetres  per  second,  the 
effect  will  be  the  same  as  a  current  of  the  value  qv.  Con- 
vection currents,  consisting  of  streams  of  electrified  particles, 
are  also^acted  upon  by  magnets.  The  convective  discharges 
in  vacuum-tubes  (Art.  342)  can  be  drawn  aside  by  a  magnet, 
or  caused  to  rotate  around  a  magnet-pole.  The  brush  dis- 
charge (Art.  340)  when  taking  place  in  a  strong  magnetic 
field  is  twisted.  The  electric  arc  (Art.  486)  also  behaves 
like  a  flexible  conductor,  and  can  be  attracted  or  repelled 
laterally  by  a  magnet-pole.  Two  stationary  positively- 
electrified  particles  repel  one  another,  but  two  parallel  cur- 
rents attract  one  another  (Art.  421),  and  if  electrified  particles 
flowing  along  act  like  currents,  there  should  be  an  (electro- 
magnetic) attraction  between  two  electrified  particles  mov- 
ing along  side  by  side  through  space.  According  to  Max- 
well's theory  (Art.  609)  the  electrostatic  repulsion  will  be 
just  equal  to  the  electromagnetic  attraction  when  the  par- 
ticles move  with  a  velocity  equal  to  the  velocity  of  light. 

Hall  discovered  in  1879  that  when  a  powerful  magnet  is 
made  to  act  upon  a  current  flowing  along  in  a  strip  of  very 
thin  metal,  the  equipotential  lines  are  no  longer  at  right 
angles  to  the  lines  of  flow  of  the  current  in  the  strip.  This 
action  appears  to  be  connected  with  the  magnetic  rotation 
of  polarized  light  (Art.  613),  the  coefficient  of  this  transverse 
thrust  of  the  magnetic  field  on  the  current  being  feebly  +  in 
gold,  strongly  -f  in  bismuth,  and  —  in  iron,  and  immensely 


CH.  v.  430]  AMPERE'S  THEORY   OF  MAGNETISM          399 

strong  negatively  in  tellurium.  It  was  shown  by  the  author, 
and  about  the  same  time  by  Righi,  that  those  metals  which 
manifest  the  Hall  effect  undergo  a  change  in  their  electric 
resistance  when  placed  in  the  magnetic  field.  The  resistance 
of  bismuth  increases  so  greatly  that  it  affords  a  way  of 
measuring  the  strength  of  magnetic  fields  (Art.  364). 

430.  Ampere's  Theory  of  Magnetism.  —  Ampere,  finding 
that  solenoids  (such  as  Fig.  218)  act  precisely  as  magnets, 
conceived  that  all  magnets  are  simply  collections  of  currents, 
or  that  around  every  individual  molecule  of  a  magnet  an 
electric  current  is  ceaselessly  circulating.  We  know  that 
such  currents  could  not  flow  perpetually  if  there  were  any 
resistance  to  them,  and  we  know  that  there  is  resistance  when 
electricity  flows  from  one  molecule  to  another.  As  we  know 
little  about  the  interior  of  molecules  themselves,  we  cannot 
assert  that  Ampere's  supposition  is  impossible.  Since  a 
whirlpool  of  electricity  acts  like  a  magnet,  there  seems  in- 
deed reason  to  think  that  magnetic  molecules  may  be  merely 
made  up  of  rotating  portions  of  electrified  matter,  or  of 
electrons  in  circulation.  See  Art.  637. 


CHAPTER  VI 

MEASUREMENT   OF   CURRENTS,    ETC. 

LESSON  XXXIII.  —  Ohm's  Law  and  its  Consequences 

431.  Law  of  Dr.  Ohm.  —  Every  conductor  and  every 
circuit  offers  a  certain  resistance  to  the  flow  of  electricity 
through  it.  When  an  electromotive-force  is  applied  to  a 
circuit  it  causes  a  current  to  flow  in  the  circuit,  but  the 
strength  of  the  resulting  current  depends  not  only  on  the 
amount  of  the  electromotive-force  but  on  the  resistance  of 
the  circuit.  In  Art.  206  the  law  discovered  by  Dr.  G.  S. 
Ohm  was  stated  in  the  following  terms :  —  The  strength  of 
the  current  varies  directly  as  the  electromotive-force,  and  in- 
versely as  the  resistance  of  the  circuit. 

Using  the  units  adopted  by  practical  electricians,  and  ex- 
plained in  Art.  381,  we  may  now  restate  Ohm's  law  in  the 
following  definite  manner :  —  The  number  of  amperes  of  cur- 
rent flowing  through  a  circuit  is  equal  to  the  number  of  volts  of 
electromotive-force  divided  by  the  number  of  ohms  of  resistance. 

Or 

amperes  =  volts  •*•  ohms, 

i  =  E/R. 

Example.  —  Let  an  electromotive-force  of  100  volts  be  applied 
to  a  circuit,  the  resistance  of  which  is  4  ohms ;  the  result- 
ing current  will  be  100  -J-  4,  that  is  25  amperes. 

Transforming  the  equation  we  may  also  write  Ohm's  law 
in  the  following  fashion  — 

E  =  i  X  R ; 

or,  the  number  of  volts  needed  to  send  a  prescribed  current 
t  through  a  circuit,  the  resistance  of  which  is  known  to  be  R, 
is  found  by  multiplying  together  i  and  R. 

400 


CH.  vi.  431]  OHM'S   LAW  401 

Example.  —  How  many  volts  are  required  to  send  a  current  of 

12  amperes  through  a  resistance  of  9  ohms  f 
Answer.  —  12  X  9  =  108  volts. 

A  third  possible  form  of  Ohm's  law  is  — 

R. 


Example.  —  If  an  electromotive-force  of  100  volts  sends  a 
current  of  0'5  ampere  through  a  glow-lamp,  what  is  the 
resistance  of  that  lamp  ? 

Answer.  —  100  -5-  0'5  =  200  ohms. 

The  law  in  its  application  is  not  always  quite  so  simple. 
If  we  apply  it  to  a  whole  circuit  we  must  consider  both  the 
total  E  and  the  total  R.  For  if  a  number  of  cells  are  used 
and  the  circuit  be  made  up  of  a  number  of  different  parts 
through  all  of  which  the  current  must  flow,  we  have  to  take 
into  account  not  only  the  electromotive-forces  of  the  cells, 
but  their  resistances,  as  well  as  the  resistances  of  other  parts 
of  the  circuit.  For  example,  the  current  may  flow  from  the 
zinc  plate  of  the  first  cell  through  the  liquid  to  the  carbon 
plate,  then  through  a  connecting  wire  or  screw  to  the  next 
cell,  through  its  liquid,  through  the  connecting  screws  and 
liquids  of  the  rest  of  the  cells,  then  through  a  wire  to  a  gal- 
vanometer, then  through  the  coils  of  the  galvanometer,  then 
perhaps  through  an  electrolytic  cell,  and  finally  through  a 
return  wire  to  the  zinc  pole  of  the  battery.  In  this  case 
there  are  a  number  of  separate  electromotive-forces  all  tend- 
ing to  produce  a  flow,  and  a  number  of  different  resistances, 
each  obstructing  the  flow  and  adding  to  the  total  resistance. 
If  in  such  a  case  we  knew  the  separate  values  of  all  the 
different  electromotive-forces  and  all  the  different  resistances 
that  are  in  series  we  could  calculate  what  the  current  would 
be,  for  it  would  have  the  value  — 


e" 


•  __  Total  electromotive-force 

Total  resistance 
2D 


402  ELECTRICITY  AND   MAGNETISM     [PT.  n.  431 

Example.  —  Let  there  be  5  cells  in  series  each  having  e  =  1*4 
volts,  and  each  an  internal  r  =  0'4  ohm;  and  let  the 
external  part  of  circuit  have  resistance  3  ohms.  Total 
E  =  7  volts  ;  total  R  =  5  ohms.  Current  i  will  be  If 
amperes. 

If  any  one  of  the  cells  were  set  wrong  way  round  its  electro- 
motive-force would  oppose  that  of  the  other  cells  ;  an  oppos- 
ing electromotive-force  must  therefore  be  subtracted,  or 
reckoned  as  negative  in  the  algebraic  sum.  The  "  polariza- 
tion "  (Arts.  183  and  566)  which  occurs  in  battery  cells  and 
in  electrolytic  cells  after  working  for  some  time  is  an  oppos- 
ing electromotive-force,  and  diminishes  the  total  of  the  elec- 
tromotive-forces in  the  circuit.  So,  also,  the  induced  back 
E.M.F.  which  is  set  up  when  a  current  from  a  battery  drives 
an  electric  motor  (Art.  455)  reduces  the  strength  of  the  work- 
ing current;  in  such  case,  if  E  is  the  electromotive-force  of 
the  battery,  e  the  opposing  electromotive-force,  and  R  the 
total  resistance,  we  shall  have 


R 

Example.  —  Suppose  the  battery  to  generate  current  at  25 
volts,  and  the  motor  to  generate  a  back  electromotive- 
force  of  20  volts,  and  the  total  resistance  to  be  2£  ohms, 
there  will  be  a  current  of  2  amperes. 

But  we  may  apply  Ohm's  law  to  a  part  of  a  circuit.  If  e 
represents  the  difference  of  potential  between  two  ends  of  a 
conductor  of  resistance  r,  the  current  i  in  it  must  be  =  e/r. 
Or,  to  put  it  the  other  way  round,  the  electromotive-force 
needed  to  drive  i  amperes  through  a  resistance  of  r  ohms 
will  be  e  —  ri  volts. 

Consider  the  case  of  a  circuit  of  which  the  resistance  is 
made  up  of  two  parts,  an  external  resistance  R  consisting  of 
wires,  lamps,  etc.,  and  of  a  smaller  resistance  r  internal  to 
the  battery  or  dynamo  (viz.  the  resistance  of  the  liquids  in 


CH.  vi.  432]  RESISTANCE  403 

the  cells,  or  of  the  wire  of  the  armature).     Then  if  E  is  the 
whole  electromotive-force  we  shall  have  as  current 

E 


R+r 

or  i(R+r)  =  E; 

or  again  iR  +  ir  =  E. 

This  means  in  words  that  the  total  volts  may  be  considered 
as  being  employed  partly  in  driving  the  current  through  the 
external  resistance  R,  partly  in  driving  the  current  through 
the  internal  resistance  r.  '  This  latter  part  of  the  electro- 
motive-force is  called  the  lost  volts;  the  remainder  being  the 
useful  or  externally  available  volts,  that  would  be  measur- 
able by  a  voltmeter  (Art.  237),  set  across  the  terminals.  If 
we  call  the  available  volts  V  we  may  write  V  =  t'R,  whence 

V  =  E  -  ir ; 

or  in  words :  the  volts  as  measured  at  the  terminals  of  a  cell 
or  dynamo  are  less  than  the  whole  E.M.F.  generated  therein ; 
being  equal  to  the  whole  E.M.F.  less  the  lost  volts.  The 
lost  volts  being  proportional  to  internal  resistance  it  is 
obviously  best  to  keep  all  internal  resistances  as  low  as  pos- 
sible. Only  when  the  cell  is  giving  no  current  are  the  exter- 
nal volts  V  equal  to  the  whole  E.M.F. ;  for  when  i  =  o,  ir 
is  also  =  o. 


Example.  —  A  dynamo  is  designed  to  generate  its  currents 
with  an  electromotive-force  of  105  volts.  The  internal 
resistance  of  its  armature  is  ^  ohm.  When  it  is  giving 
out  current  of  120  amperes,  the  lost  volts  will  be  120  X  -fa 
=  4  volts.  Consequently  the  volts  available  in  the 
external  circuit  will  be  only  101. 

Since      i  =      E      =  -  it  follows  also  that  V  =  E;  R 


R  R+r 

432.  Resistance.  —  Resistance  is  the  name  given  to  that 
property  of  materials  by  virtue  of  which  they  obstruct  the 
steady  t  flow  of  electricity  through  them,  and  fritter  down 


404  ELECTRICITY   AND   MAGNETISM         [PT.  n.  432 

into  heat  the  energy  of  the  current.  The  resistance  of  any 
conductor  or  circuit  is  measured  by  the  ratio  between  the 
volts  applied  to  its  terminals  and  the  amperes  which  result 
therefrom.  It  is  found  that  the  resistance  of  a  metal  wire, 
if  kept  at  an  unvarying  temperature,  is  the  same  whether  a 
large  current  or  a  small  current  be  flowing  through  it.  For 
example,  if  a  wire  has  a  resistance  such  that  when  a  differ- 
ence of  potential  of  10  volts  is  applied  to  its  ends  a  current 
of  2  amperes  flows  through  it  (its  resistance  being  5  ohms), 
it  will  be  found  that  if  1  volt  is  applied  the  current  will  be 
0-2  ampere,  the  ratio  between  volts  and  amperes  being  5  as 
before,  provided  the  temperature  is  kept  the  same.  Resist- 
ance of  a  given  conductor  is  in  fact  constant  so  long  as  its 
physical  properties  are  unaltered.  In  certain  non-metallic 
conductors,  as  for  example  the  arc  (Art.  486),  resistance  is 
not  a  constant  but  alters  with  the  strength  of  the  current 
that  is  being  used. 

The  unit  of  resistance,  or  ohm,  is  a  standard  chosen  in 
order  that  the  resistances  of  other  conductors  may  be  ex- 
pressed in  definite  numbers.  The  definition  of  it  is  given  in 
Art.  381.  It  is  convenient  to  remember  that  100  yards  of 
ordinary  iron  telegraph-wire  has  roughly  a  resistance  about 
1  ohm.  Or,  again,  a  thin  copper  wire  1  inch  long  and  y^r 
inch  in  diameter  has  a  resistance  of  almost  exactly  1  ohm  at 
65°  C. 

A  resistance  of  a  very  great  number  of  ohms  is  called  a 
high  resistance,  and  one  which  is  only  a  few  ohms  or  a  frac- 
tion of  an  ohm  is  called  a  low  resistance.  A  resistance  of 
one  million  ohms  is  called  a  megohm:  a  resistance  of  one 
millionth  of  one  ohm  is  called  a  microhm. 

Resistances  in  a  circuit  may  be  of  two  kinds  —  first,  the 
resistances  of  the  conductors  (metals,  alloys,  liquids)  them- 
selves; second,  the  resistances  due  to  imperfect  contact  at 
points.  The  latter  kind  of  resistance  is  affected  by  pressure, 
for  when  the  surfaces  of  two  conductors  are  brought  into 
more  intimate  contact  with  one  another,  the  current  passes 


CH.  vi.  432]  RESISTANCES  405 

more  freely  from  one  conductor  to  the  other.  The  contact- 
resistance  of  two  copper  conductors  may  vary  from  infinity 
down  to  a  small  fraction  of  an  ohm,  according  to  the  pres- 
sure. The  variation  of  resistance  at  a  point  of  imperfect 
contact  is  utilized  in  telephone  transmitters  (Art.  594). 
The  conduction  of  powdered  metals  is  remarkable.  A  loose 
heap  of  filings  scarcely  conducts  at  all,  owing  to  the  want 
of  cohesion,  or  to  the  existence  of  films  of  air  or  dust.  But, 
as  discovered  independently  by  Calzecchi-Onesti  and  Branly, 
it  becomes  instantly  a  good  conductor  if  an  electric  spark  is 
allowed  to  occur  anywhere  within  a  few  yards  of  it  (see  Arts. 
606  and  626).  The  resisting  films  of  air  are  broken  down 
by  minute  internal  discharges  in  the  mass.  A  very  slight 
agitation  by  tapping  at  once  makes  the  powder  non-con- 
ductive. The  resistance  of  a  wire  is  the  same  whether  the 
current  in  it  is  flowing  in  either  direction.  There  are  cer- 
tain crystalline  substances  such  as  galena  and  carborundum 
which  appear  to  possess  unilateral  conductivity,  that  is,  they 
conduct  better  in  one  direction  than  in  the  opposite.  They 
can  be  used  as  electric  valves  (see  Art.  634). 

For  the  purpose  of  regulating  the  flow  of  currents,  and  for 
electrical  measurements  (Art.  443),  variable  resistances  are 
employed.  Resistance  coils  (Art.  446) 
are  sets  of  coils  made  each  of  a  definite 
value  in  ohms,  of  which  one  or  more 
can  be  inserted  in  the  circuit  at  will. 
Rheostats  consist  of  easily-adjustable 
resistances,  the  length  of  wire  in  cir-  FIG.  235.— A  simple 

.,    ,      .  .     ,  ,  .  ,  „  Rheostat. 

cuit  being  varied  by  turning  a  handle, 

or  moving  a  sliding  contact.  In  some  cases  the  rheostat 
wire  is  wound  off  and  on  to  a  roller.  In  others  a  handle 
(Fig.  235)  moving  over  a  number  of  metal  studs  varies  the 
amount  of  resistance-wire  through  which  the  current  must 
flow.  Carbon  rheostats  consist  of  a  number  of  little  plates 
of  hard  carbon,  about  3  inches  square,  arranged  in  a  pile, 
with  a  screw  to  reduce  their  resistance  by  squeezing  them 


406  ELECTRICITY   AND   MAGNETISM     [PT.  n.  433 

together  into  better  contact.     Fig.  236  shows  a  very  con- 
venient  laboratory    rheostat   having   a  resistance   wire  of 

constant  an  alloy  (Art. 
436)  wound  non-induc- 
tively  (Art.  446)  upon  a 
slate  block,  and  pro- 
vided with  a  sliding 
contact  to  bring  into 

FIG.  236.  —  Sliding  Contact  Rheostat.  circuit    more    Or    leSS    of 

the  wire. 

433.  Laws  of  Resistance.  —  The  following  are  the  laws 
of  the  resistance  of  conductors  :  — 

(i.)  The  resistance  of  a  conducting  wire  is  proportional  to 
its  length.  If  the  resistance  of  a  mile  of  iron  telegraph- 
wire  be  17  ohms,  that  of  50  miles  will  be  50  X  17 
=  850  ohms. 

(ii.)  The  resistance  of  a  conducting  wire  is  inversely  propor- 
tional to  the  area  of  its  cross-section,  and  therefore  in 
the  usual  round  wires  is  inversely  proportional  to  the 
square  of  its  diameter.  Ordinary  telegraph-wire  is 
.  about  £  of  an  inch  thick ;  a  wire  twice  as  thick  would 
conduct  four  times  as  well,  having  four  times  the  area 
of  cross-section ;  hence  an  equal  length  of  it  would 
have  only  J  the  resistance. 

(iii.)  The  resistance  of  a  conducting  wire  of  given  length  and 
thickness  depends  upon  the  material  of  which  it  is 
made  —  that  is  to  say,  upon  the  specific  resistance,  or 
resistivity,  of  the  material. 

If  the  length  of  a  wire  be  I  centimetres,  and  its  area  of 
section  A  square  centimetres,  and  the  resistivity  of  the 
material  be  p,  then  its  resistance  R  will  be 

R  =  lp/ A. 

Example.  —  Find  the  resistance  of  a  platinoid  wire  of  section 
0*004  sq.  cm.,  and  200  cm.  long;  for  platinoid  the  resis- 
tivity p  =  32-5  X  10-6. 

Answer.  —  R  =  1*625  ohms. 


CH.  vi.  434-436]  RESISTIVITY  407 

434.  Conductance  and  Resistance.  —  The  term  conduct- 
ance is  used  as  the  inverse  of  resistance ;  a  conductor  whose 
resistance  is  r  ohms  is  said  to  have  a  conductance  of  1/r. 
The  unit  of  conductance  is  called  the  Siemens  (formerly  called 
"mho"}.     When  a  number  of  conductors  are  in  parallel 
with  one  another  their  united  conductance  is  the  sum  of  their 
separate  conductances. 

The  conductance  of  a  prism  of  which  the  length  is  1  cm. 
and  the  section  is  1  sq.  cm.,  is  called  its  conductivity  or  specific 
conductance. 

The  resistance  of  a  prism  of  length  1  cm.  and  section  1  sq. 
cm.  is  sometimes  called  its  resistivity  or  specific  resistance. 

435.  Resistivity.  —  The  resistivity  of  a  substance  is  most 
conveniently  stated  as  the  resistance  (in  millionths  of  an 
ohm)  of  a  centimetre  cube  of  the  substance.     The  Table  on 
p.  409  also  gives  the  relative  conductance  when  that  of 
copper  is  taken  as  100. 

Weight  for  weight,  aluminium  is  a  better  conductor  than 
silver,  and  nearly  twice  as  good  as  copper. 

It  is  found  that  those  substances  that  possess  r,  high  con- 
ducting power  for  heat  are  also  the  best  conductors  of  elec- 
tricity, but  the  ratio  of  these  conductivities  is  not  constant ; 
it  varies  as  the  absolute  temperature. 

Liquids  fall  under  three  heads:  (1)  molten  metals  and 
alloys,  which  conduct  simply  as  metals  without  undergoing 
any  decomposition  or  chemical  change ;  (2)  fused  salts  and 
solutions  of  salts  and  acids,  which  undergo  chemical  decom- 
position, and  conduct  only  by  electrolysis  (Art.  252),  such 
liquids  are  called  electrolytes;  (3)  insulators,  such  as  the  oils, 
turpentine,  etc.,  and  bromine.  Liquid  electrolytes  are 
worse  conductors  than  metals;  gases,  including  steam,  are 
perfect  non-conductors,  except  when  ionized ;  that  is,  when 
so  dissociated  as  to  admit  of  discharge  by  convection  through 
them  (Art.  332). 

436.  Effects  of  Heat  on  Resistance.  —  Changes  of  tem- 
perature affect  temporarily  the  conducting  power  of  metals. 


408  ELECTRICITY   AND   MAGNETISM      [PT.  n.  436 

Nearly  all  the  pure  metals  increase  their  resistance  about  0.4 
per  cent  for  a  rise  of  1°  C.  in  temperature,  or  about  40  per 
cent  when  warmed  100°.  When  cooled  in  liquid  air  the 
resistance  is  found  to  fall  greatly.  A  copper  wire  which  at 
0°  had  a  resistance  of  17-5  ohms  fell  to  1-65  ohms  at  -  201° 
C.  Dewar  and  Fleming  find  all  pure  metals  to  lower  their 
resistance  as  though  at  -  273°  C.  (absolute  zero  of  tempera- 
ture) they  would  become  perfect  conductors.  Kamer- 
lingh-Onnes  finds  that  at  the  temperature  of  liquid  helium 
( —  269°  C.)  the  metals  tin  and  lead  lose  all  appreciable 
resistance  and  become  super-conductors.  The  very  small 
residual  resistance  at  this  temperature  was  found  to  be 
2  X  10  10  times  smaller  than  at  the  ordinary  temperature; 
so  that  a  current  induced  in  a  closed  coil  of  lead  wire  persisted 
for  some  hours  with  only  a  small  diminution  of  strength. 
But  this  current  was  instantaneously  destroyed  on  lifting 
the  coil  out  of  the  helium.  The  resistance  of  carbon,  unlike 
that  of  the  metals,  diminishes  on  heating.  The  filament  of 
a  carbon  glow-lamp,  which  when  cold  was  230  ohms,  was 
only  150  when  white  hot.  German-silver  and  other  alloys 
do  not  show  so  much  change,  hence  they  are  used  in  making 
standard  resistance  coils.  The  temperature-coefficient  of 
German-silver  is  only  0-00044  for  1°  C.,  or  TV  that  of  the 
pure  metals.  Platinoid  and  platinum-silver  have  about 
0-00011  for  their  coefficient.  Other  alloys,  such  as  man- 
ganin,  constantan  ("  Eureka  "),  have  a  temperature-coeffi- 
cient which  is  practically  zero.  Iron  is  remarkable  in  that 
its  temperature-coefficient  which  is  about  0-0005  at  ordinary 
temperatures  suddenly  increases  to  about  three  times  that 
value  when  the  temperature  rises  to  about  855°  (or  710°  for 
steel).  This  great  increase  of  resistivity  makes  it  useful  as 
the  material  for  a  ballasting  resistance  (Art.  485).  Those 
liquids  which  only  conduct  by  being  electrolyzed  (Art.  250) 
conduct  better  as  the  temperature  rises.  The  property  of 
changing  resistance  with  temperature  is  now  used  for  measur- 
ing furnace  temperatures  in  Callendar's  platinum  pyrometer. 


CH.  vi.  436] 


RESISTIVITY 


409 


TABLE    OF   RESISTIVITY 


SUBSTANCE 

RESISTIVITY 
(MICROHMS  op 
1  CM.  CUBE) 

METRES 
PER  OHM, 

IF  OP  1 

SQ.  MM. 
SECTION 

RELATIVE 
CONDUCTANCE 

Metals  atO°C. 

Copper  (annealed)  .     . 

1-570 

63-70 

100 

„        (hard)     .     .     . 

1-603 

62-38 

9S-1 

Silver  (annealed)      .     . 

1-492 

67-03 

105 

„      (hard)        .     .     . 

1*620 

6173 

98 

Gold 

2  '077 

48"15 

76 

Aluminium  (annealed) 

2-889 

34-61 

54 

Platinum    

8*982 

11-13 

17 

Iron  (pure)     .... 

9-638 

10-37 

16 

Iron  (telegraph-wire)    . 

15 

6-66 

10 

Lead 

19*63 

5*09 

8"3 

Mercury     

94-34 

1-06 

1-6 

Selenium    

6  X  1010 

Carbon  (graphite)    .     . 

2400  to  42,000 

„        (arc  light)    .     . 

about  4000 

Alloys. 

German-silver     .     .     . 

20-76 

4-22 

7'6 

(Cu  60,  Zn  26,  Ni  14) 

Platinum-silver   .     .     . 

2-4 

41-66 

6-5 

(Pt  67,  Ag  33) 

Platinoid    

32-5 

3'08 

4'8 

(Cu  59,  Zn  25.5,  Ni  14, 

W  1  5) 

Manganin       .... 

47-5 

2-10 

3*3 

(Cu  84,  Ni  12,  Mn  3.5) 

Constantan  (Eureka) 

50 

2 

3*1 

(Cu  60,  Ni  40) 

Liquids  at  18°  C. 

Pure  Water     .... 

26.5  X  108 

Dilute  H2SO4,  5%   .     . 

486  x  104 

less  than  one 

„       H2S04,  30%      . 

137  X  104 

millionth  part 

„      H2SO4,  80%      . 

918  X  104 

„       ZnSO4,  24%      . 

214  X  105 

„       HNO3,  30%       . 

129  X  104 

Insulators. 

Glass  at  20°  C.    .     .     . 

91   X  1018 

Glass  at  200°  C.       .     . 

22'7  x  1012 

less   than   one 

Gutta-percha  24°  C.     . 

4'5  X  1020 

billionth 

410  ELECTRICITY  AND   MAGNETISM     [pr.  n.  437 

The  bolometer  used  by  Langley  in  researches  on  radiant  heat 
depends  on  the  same  property.  It  consists  of  a  strip  or  grid 
of  platinum  wire  blackened  on  one  edge  so  as  to  absorb  the 
radiation  ;  the  resulting  increase  in  the  resistance  of  the  wire 
being  measured  by  a  Wheatstone's  Bridge  (Art.  445).  Some 
substances  show  an  increase  of  resistivity,  iron  slightly, 
bismuth  considerably,  when  placed  in  a  magnetic  field.  The 
effect  of  light  in  varying  the  resistance  of  selenium  is  stated 
in  Art.  617. 

437.  Insulators.  —  The  name  insulators  is  given  to  ma- 
terials which  have  such  high  resistances  that  they  can  be 
used  as  non-conductors.  They  differ  much  in  their  mechani- 
cal qualities  as  well  as  in  their  insulation-resistance.  They 
may  be  classed  under  several  heads  :  (1)  Vitreous,  including 
glass  of  all  kinds,  slags,  and  quartz;  (2)  Stony,  including 
slate,  marble,  stoneware,  steatite,  porcelain,  mica,  asbestos ; 
(3)  Resinous,  including  shellac,  resin,  beeswax,  pitch,  various 
gums,  bitumen,  ozokerit,  and  amber;  (4)  Elastic,  including 
india-rubber,  gutta-percha,  ebonite;  (5)  Oily,  including 
various  oils  and  fats  of  animal  and  vegetable  origin,  as  well 
as  solid  paraffin  and  petroleum  oil ;  (6)  Cellulose,  including 
dry  wood  and  paper,  and  preparations  of  paper,  such  as 
"  fibre  "  and  celluloid.  All  these  materials  decrease  their 
resistance  enormously  as  the  temperature  rises,  and  in 
general  become  fairly  good  conductors  as  soon  as  any  chemi- 
cal change  begins ;  some  of  them  (as  glass)  conduct  as 
electrolytes  as  soon  as  they  soften.  Micanite  is  a  name  given 
to  flaked  mica  cemented  together  by  shellac  under  pressure 
while  warm.  The  resistance  of  insulators  is  not  independent 
of  the  voltage.  For  example,  Evershed  observed  that  when 
tested  at  50  volts  the  resistance  of  the  insulating  cotton 
covering  between  certain  copper  wires,  after  being  dried  for 
two  hours  at  150°  C.,  was  25  megohms,  but  was  only  9 
megohms  when  tested  at  500  volts.  Moisture  is  largely 
responsible  for  these  variations  of  insulation  resistance. 

The  name  insulators  is  also  given  to  the  articles  used  for 


CH.  vi.  438]  CIRCUIT   CALCULATIONS  411 

the  insulating  supports  of  stoneware,  porcelain,  or  glass  on 
which  telegraph  wires  are  carried  (Art.  580). 

438.    Typical  Circuit.  —  Let  us  consider  the  typical  case 
of  the  circuit  shown  in  Fig.  237,  in  which  a  battery,  ZC,  is 
joined  up  in  circuit  with  a  gal- 
vanometer   by    means    of    wires 
whose  resistance  is  R.     The  total 
electromotive-force  of  the  battery 
we  will  call  E,  and  the  total  in- 
ternal resistance  of  the  liquids  in 
the  cells  r.     The  resistance  of  the 
galvanometer  coils  may  be  called  FIG.  237. 

G.     Then,  by  Ohm's  law  :  - 

E 
R  +r  +  G' 

The  internal  resistance  r  of  the  liquids  of  the  battery  bears 
an  important  relation  to  the  external  resistance  of  the  circuit 
(including  R  and  G),  for  on  this  relation  depends  the  best 
way  of  arranging  the  battery  cells.  Suppose,  for  example, 
that  we  have  a  battery  of  50  small  Daniell's  cells  at  our  dis- 
posal, of  which  we  may  reckon  the  electromotive-force  as 
one  volt  (or,  more  accurately,  1-07  volt)  each,  and  each 
having  an  internal  resistance  of  two  ohms.  If  we  have  to 
use  these  cells  on  a  circuit  where  there  is  already  of  necessity 
a  high  resistance,  we  should  couple  them  up  "  in  series  " 
rather  than  in  parallel.  For,  supposing  we  have  to  send  our 
current  through  a  telegraph  line  100  miles  long,  the  external 
resistance  R  will  be  (reckoning  13  ohms  to  the  mile  of  wire) 
at  least  1300  ohms.  Through  this  resistance  a  single  such 
cell  would  give  a  current  of  less  than  one  milliampere,  for 

here    E  =  1,    R  =  1300,    r  =  2,    and    therefore   i  =  _.^ 

R  +  r 

=  IOAA   i   o  =  :T^7^  °f  an  amPei>e,  a  current  too  weak  to 
work  an  ordinary  telegraph  instrument. 


412  ELECTRICITY  AND  MAGNETISM      [PT.  n.  438 

With  fifty  such  cells  in  series  we  should  have  E  =  50, 
r  =  100,  and  then 


1300  +  100 

amperes.  In  telegraph  work,  where  the  instruments  require 
a  current  of  5  to  10  milli-amperes  to  work  them,  it  is  usual 
to  reckon  an  additional  Daniell's  cell  for  every  5  miles  of 
line,  each  instrument  in  the  circuit  being  counted  as  having 
as  great  a  resistance  as  10  miles  of  wire. 

If,  however,  the  resistance  of  the  external  circuit  be  small, 
such  arrangements  must  be  made  as  will  keep  the  total 
internal  resistance  of  the  battery  small.  Suppose,  for  ex- 
ample, we  wish  merely  to  heat  a  small  piece  of  platinum  wire 
to  redness,  using  stout  copper  wires  to  connect  it  with  the 
battery.  Here  the  external  resistance  may  possibly  not  be 
as  much  as  1  ohm.  In  that  case  a  single  cell  would  give  a 
current  of  \  of  an  ampere  (or  333  milli-amperes)  through 
the  wire,  for  here  E  =  1,  R  =  1,  and  r  =  2.  But  10  cells 
would  only  give  half  as  much  again,  or  476  milli-amperes, 
and  fifty  cells  only  495  milli-amperes,  and  with  an  infinite 
number  of  such  cells  in  series  the  current  could  not  possibly 
be  more  than  500  milli-amperes,  because  every  cell,  though 
it  adds  1  to  E,  adds  2  to  R.  It  is  clear  then  that  though 
linking  many  cells  in  series  is  of  advantage  where  there  is 
the  resistance  of  a  long  line  of  wire  to  be  overcome,  yet 
where  the  external  resistance  is  small  the  practical  advantage 
of  adding  cells  in  series  soon  reaches  a  limit. 

But  suppose  in  this  second  case,  where  the  external  re- 
sistance of  the  circuit  is  small,  we  reduce  also  the  internal 
resistance  of  our  battery  by  linking  cells  together  in  parallel, 
joining  several  zincs  of  several  cells  together,  and  joining 
also  their  copper  poles  together  (as  suggested  in  Art.  207), 
a  different  and  better  result  is  attained.  Suppose  we  thus 
join  up  four  cells.  Their  electromotive-force  will  be  no 
more,  it  is  true,  than  that  of  one  cell,  but  their  resistance 
will  be  but  J  of  one  such  cell,  or  \  an  ohm.  These  four  cells 


CH.  vi.  439]  GROUPING   OF   CELLS  413 

would  give  a  current  of  666  milli-amperes  through  an  external 
resistance  of  1  ohm,  for  if  E  =  1,  R  =  1,  and  the  internal 

resistance  be  J  of  r,  or  =  J,  then 

-p 
i  = — =  —  =  f  of  an  ampere,  or  666  milli-amperes. 

Jtv      j"~    / 

If  we  arrange  the  cells  of  a  battery  in  p  files  in  parallel, 
having  s  cells  in  series  in  each  file  (there  being  p  X  s  =  N 
similar  cells  altogether),  the  electromotive-force  of  each  file 
will  be  s  times  the  electromotive-force  E  of  each  cell,  or  sE ; 
and  the  resistance  of  each  file  will  be  s  times  the  resistance  r 
of  each  cell,  or  sr.  But  there  being  p  files  in  parallel  the 

whole  internal  resistance  will  be  only  -  of  the  resistance  of 

p 

any  one  file,  or  will  be  -r,  hence,  by  Ohm's  law,  such  a 

P 
battery  would  give  as  its  current 

sE 

i  = 


-r  +  R 
P 

439.  Best  Groupings  of  Cells.  —  If  the  question  arises  as 
to  the  best  way  of  grouping  a  given  number  of  cells,  it  must 
be  replied  that  there  are  several  best  ways. 

(1)  Grouping  for  best  Economy.  —  So  group  the  cells  that 
their  united  internal  resistance  shall  be  very  small  compared 
with  the  external  resistance.     In  this  case  the  materials  of 
the  battery  will  be  consumed  slowly,  and  the  current  will 
not  be  drawn  off  at  its  greatest  possible  strength ;  but  there 
will  be  a  minimum  waste  of  energy  (Art.  454). 

(2)  Grouping  for   greatest    Current.  —  It    can   be   shown 
mathematically  that,  for  a  given  battery  of  cells,  the  way 
of  grouping  them  that  will  give  the  largest  steady  current 
when  they  are  required  to  work  through  a  given  external 
resistance  X,  is  so  to  choose  s  and  p,  that  the  internal  resist- 

o 

ance  -r   shall   equal   the   external  resistance.     This   can   be 

P  

done  by  choosing  p  such  that  p  —  VNr  -s-  X ;    for  then  the 


414  ELECTRICITY   AND   MAGNETISM      [PT.  n.  440 

resistance  R  of  the  whole  battery  as  so  arranged,  will  be 
Nr  =  p2,  which  equals  X.  The  student  should  verify  this  rule 
by  taking  examples  and  working  them  out  for  different  group- 
ings of  the  cells.  Although  this  arrangement  gives  the  largest 
current  it  is  not  the  most  economical ;  for  if  the  internal  and 
external  resistances  be  equal  to  one  another,  the  useful  work 
in  the  outer  circuit  and  the  useless  work  done  in  heating  the 
cells  will  be  equal  also,  half  the  energy  being  wasted. 

(3)  Grouping  for  quickest  Action.  —  If  there  are  electro- 
magnets, or  other  objects  possessing  self-induction  (Art. 
501)  in  the  circuit,  which  would  tend  to  prevent  the  current 
rising  quickly  to  its  proper  value,  the  best  grouping  to  cause 
the  current  to  rise  as  quickly  as  possible  is  one  that  will 
make  the  internal  resistance  higher  than  the  external,  namely, 
put  all  the  cells  in  series  (see  Art.  504). 

440.  Long  and  Short  Coil  Instruments.  —  The  student 
will  also  now  have  no  difficulty  in  perceiving  why  a  "  long- 
coil  "  galvanometer,  or  a  "  long-coil "  electromagnet,  or 
instrument  of  any  kind  in  which  the  conductor  is  a  long  thin 
wire  of  high  resistance,  must  not  be  employed  on  circuits 
where  both  R  and  r  are  already  small.  He  will  also  under- 
stand why,  on  circuits  of  great  length,  or  where  there  is  of 
necessity  a  high  resistance  and  where  therefore  a  battery  of 
great  electromotive-force  is  employed,  "  short-coil  "  instru- 
ments are  of  little  service,  for  though  they  add  little  to  the 
resistances,  their  few  turns  of  wire  are  not  enough  to  produce 
the  required  action  with  the  small  currents  that  circulate 
in  high-resistance  circuits.  He  will  understand,  too/  why 
"  long-coil  "  instruments  are  here  appropriate  as  multiplying 
the  effects  of  the  currents  by  their  many  turns,  their  resist- 
ance, though  perhaps  large,  not  being  a  serious  addition 
to  the  existing  resistances  of  the  circuit.  The  main  point 
to  grasp  is  that  it  is  the  nature  of  the  line,  whether  of  high  re- 
sistance or  low,  which  determines  not  only  the  grouping 
of  the  battery,  but  also  what  kind  of  winding,  whether 
many  turns  of  thin  wire  or  a  few  turns  of  thick,  is  appro- 
priate in  the  instruments. 


CH.  vi.  441] 


DIVIDED   CIRCUITS 


415 


FIG.  238.  —  A  Divided  Circuit. 


441.  Divided  Circuits.  —  If  a  circuit  divides,  as  in  Fig. 
238,  into  two  branches  at  A,  uniting  together  again  at  B, 
the  current  will  also  be  divided, 
part  flowing  through  one  branch, 
part  through  the  other.  Any 
branch  which  serves  as  a  by-pass 
to  another  branch  is  termed  a 
shunt.  The  relative  strengths  of 
current  in  the  two  branches  will  be 
proportional  to  their  conductances,  i.e.  inversely  proportional 
to  their  resistances.1  Thus,  if  r  be  a  wire  of  2  ohms  resistance 
and  r'  be  3  ohms,  then  current  in  r  is  to  the  current  in  r' 
is  to  r ;  or  as  3  to  2.  Hence  f  of  the  whole  current  will  flow 
through  r,  and  f  of  the  whole  current  through  r1 '. 

The  joint  resistance  of  the  divided  circuit  between  A  and 
B  will  be  less  than  the  resistance  of  either  branch  singly, 
because  the  current  has  now  two  paths.  In  fact,  the  joint 
conductance  will  be  the  sum  of  the  two  separate  conductances. 
And  if  we  call  the  joint  resistance  R,  it  follows  that 


r'Xr 


R 

whence  R  = 


rr 


rr 


r'+r 


or,   in  words,    the  joint   re- 


sistance of  a  divided  conductor  is  equal  to  the  product  of  the  two 
separate  resistances  divided  by  their  sum. 
This  is  sometimes  called  the  law  of 
shunts,  because  each  of  the  branches 
may  be  regarded  as  a  shunt  to  the 
other.  A  simple  construction  for  find- 
ing  the  value  graphically  is  given  in 


Fig.  239.     Let  lines  representing  the  two  resistances  r  and  r' 

1  There  is  a  popular  fallacy  that  an  electric  current  "always  takes  the 
line  of  least  resistance."  It  never  does,  though  part  of  the  current  may 
flow  that  way.  It  divides  between  the  various  paths  in  proportion  to  their 
easiness.  It  is  only  spark  discharges  which  pierce  a  non-conductor  that 
can  be  said  to  take  the  line  of  least  resistance. 


416 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  442 


FIG.  240. 


be  erected  at  the  ends  of  any  base  line,  and  the  diagonals 
drawn  as  shown.  The  perpendicular  at  the  point  of  their 
intersection  will  be  the  joint  resistance  R. 
In  case  there  are  three  or  more  branches 
all  in  parallel,  as  in  Fig.  240,  the  rule  may 
be  generalized  as  follows  :  — 

The  joint  resistance  of  any  number  of  con- 
ductors in  parallel  is  the  reciprocal  of  the 
sum  of  the  reciprocals   of  the   separate  resistances. 

Kirchhoff  formulated  the  following  important  laws,  both 
of  them  deducible  from  Ohm's  law :  — 

(i.)  In  any  branching  network  of  wires  the  algebraic  sum  of 
the  currents  in  all  the  wires  that  meet  in  any  point  is 
zero. 

(ii.)  When  there  are  several  electromotive-forces  acting  at 
different  points  of  a  circuit,  the  total  electromotive-force 
round  the  circuit  is  equal  to  the  sum  of  the  resistances  of 
its  separate  parts  multiplied  each  into  the  strength  of  the 
current  that  flows  through  it. 

442.  Current  Sheets.  —  When  a  current  enters  a  wide 
conductor  it  never  takes  the  line  of  least  resistance ;  instead 
of  flowing  in  one  line  it  spreads  out 
and  flows  through  the  mass  of  the 
conductor.  When  a  current  is  led 
into  a  thin  plate  of  conducting 
matter  it  spreads  out  into  a  current 
sheet  and  flows  through  the  plate  by 
stream-lines  in  directions  that  depend 
upon  the  form  of  the  plate  and  the 
position  of  the  pole  by  which  it  re- 
turns to  the  battery.  Thus,  if  wires 
from  the  two  poles  of  a  battery  are 
brought  into  contact  with  two  neighbouring  points  A  and  B 
at  the  edges  of  a  flat  sheet  of  tinfoil,  the  current  flows,  in- 
visibly, through  the  foil  not  in  one  straight  line  from  A  to 


FIG.  241.  —  Stream-lines  of 
Current. 


CH.  vi.  443]     MEASUREMENT   OP   RESISTANCE  417 

B,  but  in  stream-lines,  Fig.  241,  which  start  out  in  all  direc- 
tions from  A,  and  curl  round  to  meet  in  B,  in  curves  very 
like  those  of  the  magnetic  lines  of  force  that  run  from  the 
N-pole  to  the  S-pole  of  a  magnet  (Fig.  69).  When  the 
earth  is  used  as  a  return  wire  to  conduct  the  telegraph 
currents  (Fig.  344),  a  similar  spreading  of  the  currents  into 
current  sheets  occurs. 


LESSON  XXXIV.  —  Electrical  Measurements 

443.  Measurement  of  Resistance.  —  The  practical  elec- 
trician has  to  measure  electrical  resistances,  electromotive- 
forces,  and  the  capacities  of  condensers.  Each  of  these 
several  quantities  is  measured  by  comparison  with  some 
ascertained  standard ;  the  particular  methods  of  comparison 
varying,  however,  to  meet  the  circumstances  of  the  case. 
Only  a  few  simple  cases  can  be  here  explained. 

Ohm's  law  shows  us  that  the  strength  of  a  current  due  to 
an  electromotive-force  falls  off  in  inverse  proportion  as  the 
resistance  in  the  circuit  increases. 

(a)  Method  of  Substitution.  —  It  is  therefore  possible  to 
compare  two  resistances  with  one  another  by  finding  out  in 
what  proportion  each  of  them  will  cause  the  current  of  a 
constant  battery  to  fall  off.  Thus,  suppose  in  Fig.  237  we 
have  a  standard  battery  of  a  few  Daniell's  cells,  joined  up 
in  circuit  with  a  wire  of  an  unknown  resistance  R,  and  with 
a  galvanometer,  we  shall  obtain  a  current  of  a  certain 
strength,  as  indicated  by  the  galvanometer  needle  experienc- 
ing a  certain  deflexion.  If  we  remove  the  wire  R,  and  sub- 
stitute in  its  place  in  the  circuit  wires  whose  resistances  we 
know,  we  may,  by  trying,  find  one  which,  when  interposed 
in  the  path  of  the  current,  gives  the  same  deflexion  on  the 
galvanometer.  This  wire  and  the  one  we  called  R  offer 
equal  resistance  to  the  current.  This  method  of  substitution 
of  equivalent  resistances  was  further  developed  by  Wheat- 
stone,  Jacobi,  and  others,  when  they  proposed  to  employ  as 


418  ELECTRICITY  AND   MAGNETISM     [PT.  n.  443 

a  standard  resistance  a  long  thin  wire  coiled  upon  a  wooden 
cylinder,  so  that  any  desired  length  of  the  standard  wire 
might  be  thrown  into  the  circuit  by  unwinding  the  proper 
number  of  turns  of  wire  off  the  cylinder,  or  by  making  con- 
tact at  some  point  at  any  desired  distance  from  the  end  of  the 
wire.  This  form  of  rheostat  was  found,  however,  to  be  less 
accurate  than  the  resistance  coils  described  below. 

(6)  Method  of  Proportional  Deflexion.  —  The  method  ex- 
plained above  can  be  used  with  any  galvanometer  of  suffi- 
cient sensitiveness,  but  if  a  tangent  galvanometer  is  available 
the  process  may  be  shortened  by  calculation.  Suppose  the 
galvanometer  and  an  unknown  resistance  R  to  be  included 
in  the  circuit,  as  in  Fig.  237,  and  that  the  current  is  strong 
enough  to  produce  a  deflexion  8 :  Now  substitute  for  R  any 
known  resistance  R',  which  will  alter  the  deflexion  to  8'; 
then  (provided  the  other  resistances  of  the  circuit  be  neg- 
ligibly small)  it  is  clear  that  since  the  strengths  of  the  cur- 
rents are  proportional  to  tan  8  and  tan  8'  respectively,  the 
resistance  R  can  be  calculated  by  the  inverse  proportion, 

tan  8  :  tan  8'  =  R7 :  R. 

(c)  Method  of  Differential  Galvanometer.  —  With  a  differ- 
ential galvanometer  (Art.  233),  and  a  set  of  standard  resist- 
ance coils,  it  is  easy  to  measure  the  re- 
S^ance  °f  a  conductor.  Let  the  circuit 
divide  into  two  branches,  as  in  Fig.  242, 
so  that  part  of  the  current  flows  through 
the  unknown  resistance  and  round  one  set 
of  coils  of  the  galvanometer,  the  other  part 
of  the  current  being  made  to  flow  through 
the  known  resistances  and  then  round  the 

°ther  ^  °f  C°ils  in  the  Opposing  direction. 

by  Differential  Gal-    When  we  have  succeeded  in  matching  the 

vanometer.  •....* 

unknown  resistance  by  one  equal  to  it  from 
amongst  the  known  resistances,  the  currents  in  the  two 
branches  will  be  equal,  and  the  needle  of  the  differential 


CH.  vi.  444]  FALL   OF   POTENTIAL  419 

galvanometer  will  show  no  deflexion.     This  null  method  is 
very  exact. 

(d)  Bridge  Methods.  —  The  best  of  all  the  ways  of  measur- 
ing resistances  is,  however,  with  the  important  instrument 
known  as  Wheatstone's  Bridge,  described  below  in  Art.  445. 

(e)  Condenser  Methods.  —  To  measure  very  high  resist- 
ances the  plan  may  be  adopted  of  charging  a  condenser  from 
a  standard  battery  for  a  definite  time  through  the  resistance, 
and  then  ascertaining  the  accumulated  charge  by  discharg- 
ing it  through  a  ballistic  galvanometer   (Art.   234).     The 
higher  the  resistance,  the  less  is  the  quantity  of  electricity 
which  it  will  allow  to  flow  into  the  condenser  during  the  time 
of  charge.     Or  in  another  method  the  condenser  is  allowed 
to  discharge  itself  slowly  through  the  high  resistance,  and 
the  time  taken  by  the  potential  to  fall  through  any  given 
fraction  of  its  original  value  is  observed.     This  time  is  pro- 
portional to  the  resistance,  to  the  capacity,  and  to  the  log- 
arithm of  the  given  fraction. 

444.  Fall  of  Potential  along  a  Wire.  —  To  understand  the 
principle  of  Wheatstone's  Bridge  we  must  explain  a  pre- 
liminary point.  If  the  electric  potential  of  different  points 
of  a  circuit  be  examined  by  means  of  an  electrometer,  as 
explained  in  Art.  308,  it  is  found  to  decrease  all  the  way 
round  the  circuit  from  the  +  pole  of  the  battery,  where  it  is 
highest,  down  to  the  —  pole,  where  it  is  lowest.  If  the  cir- 
cuit consist  of  one  wire  of  uniform  thickness,  which  offers, 
consequently,  a  uniform  resistance  to  the  current,  it  is  found 
that  the  potential  falls  uniformly;  if,  however,  one  part  of 
the  circuit  resists  more  than  another,  it  is  found  that  the 
potential  falls  most  rapidly  along  the  conductor  of  greatest 
resistance.  If  with  a  suitable  voltmeter,  either  an  electrom- 
eter or  a  fine-wire  galvanometer  having  a  high  resistance 
in  series  with  it,  we  explore  the  fall  of  potential  between  two 
points  a  and  6  of  a  circuit  (Fig.  243),  we  shall  find  in  every 
case  the  fall  of  potential  proportional  to  the  resistance  be- 
tween those  two  points.  For  V  =  iH,  and  therefore,  for  the 


420 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  445 


same  i,  the  V  across  any  part  is  proportional  to  the  R  of  that 
part.  We  know,  for  example,  that  when  we  have  gone  round 
the  circuit  to  a  point  where  the  potential  has  fallen  through 
half  its  value,  the  current  has  at  that 
point  gone  through  half  the  resist- 
ances. The  best  way  to  measure  a 
very  large  current  is  to  measure  (with 
voltmeter  arrangement  of  galvanom- 
eter) the  drop  of  potential  it  pro- 
duces when  sent  through  a  known 
very  low  resistance  such  as  a  strip  of  platinoid  having 
exactly  T^Vu-  ohm  resistance  between  two  measured  points. 
To  measure  a  very  small  resistance,  it  should  be  put  in  series 
(Fig.  244),  with  another  known  very  small  resistance,  and 
the  drops  of  potential,  when  the  same  current  flows  through 
both,  are  compared  :  the  resistance  of  each  being  as  the  drop 


FIG.  243.  —  Fall  of  Potential 
along  a  Wire. 


FIG.  244.  —  Measurement  of  Resistance  by  Drop  of  Potential. 

in  potential  between  its  ends.  If  the  voltmeter  reading  when 
the  instrument  is  placed  across  the  ends  of  the  standard 
resistance  s  is  called  Vi,  and  the  reading  when  placed  across 
the  ends  of  the  unknown  resistance  x  is  V2,  then  x :  s :  :  V2 :  Vi. 
445.  Wheatstone's  Bridge.  —  This  instrument,  invented 
by  Christie,  and  applied  by  Wheatstone  to  measure  resist- 
ances, consists  of  a  system  of  conductors  shown  in  diagram 
in  Fig.  245.  This  circuit  of  a  battery  is  made  to  branch  at 
P  into  two  parts,  which  reunite  at  Q,  so  that  part  of  the  cur- 
rent flows  through  the  point  M,  the  other  part  through  the 


CH.  vi.  445] 


WHEATSTONE'S   BRIDGE 


421 


point  N.  The  four  conductors,  A,  B,  C,  D,  are  spoken  of 
as  the  "  arms  "  of  the  "  balance  "  or  "  bridge  " ;  it  is  by  the 
proportion  subsisting  between  their  resistances  that  the 
resistance  of  one  of  them  can  be  calculated  when  the  resist- 
ances of  the  other  three  are  known.  When  the  current  which 
flows  from  the  battery  arrives  at  P,  the  potential  will  have 
fallen  to  a  certain  value.  From  P  the  potential  of  the  cur- 
rent in  the  upper  branch  falls  to  M,  and  continues  to  fall  to  Q. 


FIG.  245.  —  Wheatstone's  Bridge. 

The  potential  of  the  lower  branch  falls  to  N,  and  again  falls 
till  it  reaches  Q.  Now  if  N  be  the  same  proportionate  dis- 
tance along  the  resistances  of  the  lower  branch  between  P 
and  Q,  as  M  is  along  the  resistances  of  the  upper  branch  be- 
tween P  and  Q,  the  potential  will  have  fallen  at  N  to  the  same 
value  as  it  has  fallen  to  at  M ;  or,  in  other  words,  if  the  ratio 
of  the  resistances  C  to  the  resistance  D  be  equal  to  the  ratio 
between  the  resistance  A  and  the  resistance  B,  then  M  and 
N  will  be  at  equal  potentials.  To  find  out  whether  they  are 
at  equal  potentials  a  sensitive  galvanometer  is  placed  in  a 
branch  wire  between  M  and  N;  it  will  show  no  deflexion 
when  M  and  N  are  at  equal  potentials;  or  when  the  four 
resistances  of  the  arms  "  balance  "  one  another  by  being  in 
proportion,  thus :  — 

A :  C  : :  B  :  D. 


422  ELECTRICITY   AND   MAGNETISM       [PT.  n.  446 

If,  then,  we  know  what  A,  B,  and  C  are,  we  can  calculate 
D,  which  will  be 


Example.  —  Thus  if  A  and  C  are  (as  in  Fig.  248)  10  ohms  and 
100  ohms  respectively,  and  B  be  15  ohms,  D  will  be 
15  X  100  4-  10  =  150  ohms. 

Note  that  balance  can  equally  be  obtained  if  the  positions 
of  the  galvanometer  and  the  battery  are  exchanged;  the 
battery  being  between  M  and  N,  while  the  galvanometer  is 
joined  from  P  to  Q. 

446.  Resistance  Coils.  —  Wires  of  standard  resistance 
are  sold  by  instrument-makers  under  the  name  of  Resistance 
Coils.  They  consist  of  coils  of  some  alloy,  german-silver, 
platinum-silver,  manganin,  or  platinoid  (see  Art.  436),  wound 
with  great  care,  and  adjusted  to  such  a  length  as  to  have  re- 
sistances of  a  definite  number  of  ohms.  In  order  to  avoid 
self-induction,  and  the  consequent  sparks  (see  Art.  501)  at 
the  opening  or  closing  of  the  circuit,  they  are  wound  in  the 
peculiar  non-inductive  manner  indicated  in  Fig.  246,  each  wire 
(covered  with  silk  or  paraffined-cotton)  being  doubled  on 
itself  before  being  coiled  up. 
Each  end  of  a  coil  is  soldered  to 
a  solid  brass  piece,  as  coil  1  to  A 
and  B,  coil  2  to  B  and  C;  the 
brass  pieces  being  themselves 
fixed  to  a  block  of  ebonite  (form- 
ing the  top  of  the  "  resistance 

box"),    With    Sufficient    rOOm    be-    FlG-  246-  -  Arrangement  of  Resist- 

.  ance  Coils. 

tween  them  to  admit  of  the  in- 

sertion of  stout  well-fitting  plugs  of  brass.  Fig.  247  shows  a 
complete  resistance  box,  as  fitted  up  for  electrical  testing,  with 
the  plugs  in  their  places.  So  long  as  the  plugs  remain  in,  the 
current  flows  through  the  solid  brass  pieces  and  plugs  with- 
out encountering  any  serious  resistance  ;  but  when  any  plug 


CH.  vi.  446] 


RESISTANCE   BRIDGES 


423 


is  removed,  the  current  can  only  pass  from  the  one  brass  piece 

to  the  other  by  traversing  the  coil  thus  thrown  into  circuit. 

The  series  of  coils  chosen  is  usually  of  the  following  numbers 

of  ohms'  resistance  —  1, 
2,  2,  5;  10,  20,  20,  50; 
100,  200,  200,  500 ;  ... 
up  to  10,000  ohms.  By 
pulling  out  one  plug  any 
one  of  these  can  be 
thrown  into  the  circuit, 
and  any  desired  whole 
number,  up  to  20,000, 
can  be  made  up  by  pull- 
ing out  more  plugs ;  thus 
a  resistance  of  263  ohms 
will  be  made  up  as  200 

+  50  +  10  +  2  +  1  by  unplugging  those  five  coils. 
It  is  usual  to  construct  Wheatstone's  bridges  with  some 

balancing  resistance  coils  in  the  arms  A  and  C,  as  well  as 


FIG.  247.  —  Resistance  Box  arranged  as  a 
Wheatstone's  Bridge. 


Fio.  248.  —  Diagram  of  Wheatstone's  Bridge. 

• 

with  a  complete  set  in  the  arm  B.  The  advantage  of  this 
arrangement  is  that  by  adjusting  A  and  C  we  determine 
the  proportionality  between  B  and  D,  and  can,  indeed, 


424  ELECTRICITY  AND   MAGNETISM     [PT.  n.  447 

measure  to  fractions  of  an  ohm.  Fig.  247  shows  a  more  com- 
plete scheme,  in  which  resistances  of  10,  100,  and  1000  ohms 
are  included  in  the  arms  A  and  C. 

Example.  —  Suppose  we  had  a  wire  whose  resistance  we 
knew  to  be  between  46  and  47  ohms,  and  wished  to  meas- 
ure the  fraction  of  an  ohm,  we  should  insert  it  at  D,  and 
make  A  100  ohms  and  C  10  ohms ;  in  that  case  D  would 
be  balanced  by  a  resistance  in  B  10  times  as  great  as  the 
wire  D.  If,  on  trial,  this  be  found  to  be  464  ohms,  we 
know  that  D  =  464  X  10  -^  100  =  46'4  ohms 

447.  Other  Patterns  of  Bridge.  —  In  practice  the  bridge 
is  seldom  or  never  made  in  the  lozenge-shape  of  the  diagrams.. 

Post-Office  Bridge.  —  The  resistance-box  of  Fig.  247  is, 
in  itself,  a  complete  "  bridge  "  of  the  Post-Office  pattern, 
the  appropriate  connexions  being  made  by  screws  at  various 
points.  In  using  the  bridge  the  battery  circuit  should  always 
be  completed  by  depressing  the  key  Ki  before  the  key  K2 
of  the  galvanometer  circuit  is  depressed,  in  order  to  avoid 
the  sudden  violent  "  throw  "  of  the  galvanometer  needle, 
which  occurs  on  closing  circuit  in  consequence  of  self-induc- 
tion (Art.  501). 

Dial  Bridge.  —  To  avoid  errors  arising  from  the  differ- 
ent numbers  of  plugs  in  use,  the  coils  of  a  bridge  are  some- 
times arranged  in  dials  —  the  units  in  one,  the  tens  of  ohms  in 
another,  and  so  forth  —  each  dial  having  but  one  plug,  or  a 
movable  arm  like  Fig.  235. 

Metre  Bridge.  —  This  is  a  simple  form  very  useful  for 
measuring  resistances  not  exceeding  a  few  hundred  ohms. 
Upon  a  long  board  is  stretched  over  a  scale  one  metre  long  a 
uniform  thin  wire  of  german-silver  or  other  alloy,  its  ends 
being  joined  to  stout  pieces  of  copper.  Here  A,  B,  C,  and  D 
are  four  resistances  joined  as  shown  by  stout  strips  of  copper. 
When  the  wire  from  the*  galvanometer  is  slid  along  the  wire 
to  such  a  point  that  there  is  no  current,  it  follows  that 


CH.  vi.  447] 


BRIDGES 


425 


Foster's  method  of  measuring  small  differences  of  resist- 
ance is  to  get  balance  at  a  certain  point  along  the  wire  (Fig. 
249),  then  interchange  A  and  B,  and  again  get  balance  at 

-lllllH 


FIG.  249.  —  Carey  Foster's  Bridge. 

another  point.  The  resistance  of  the  piece  of  wire  between 
the  two  points  of  balance  will  then  be  equal  to  the  difference 
of  the  resistances  A  and  B. 


FIG.  250.  —  Simple  Slide-wire  Bridge. 

In  a  simpler  way,  Fig.  250,  of  using  a  slide-wire  bridge,  A 
and  B  are  replaced  by  strips  of  no  appreciable  resistance,  so 

that  a  :  b  : :  C  :  D. 

If  D  is  the  unknown  resistance  and  C  a  known  resistance, 
the  ratio  of  the  lengths  a  and  6  at  once  enables  the  unknown 
resistance  to  be  calculated 


FIG.  251.  —  Slide-wire  Bridge. 


Yet  another  way  of  using  a  slide-wire  bridge  is  that  shown 
in  Fig.  251,  where  x  is  an  unknown  resistance  and  s  a  standard 


426  ELECTRICITY   AND   MAGNETISM     [PT.  n.  448 

resistance  not  differing  greatly  from  that  to  be  measured. 
If  contact  with  the  galvanometer  circuit  is  made  at  100  divi- 
sions along  the  slide-wire,  and  the  contact  c  is  moved  along 
till  balance  is  obtained,  the  number  of  divisions  y  along  the 
wire  will  give  the  value  of  £  as  a  percentage  of  s,  since  y  —  100 
X  x  -h  s. 

For  further  details  of  bridge  methods  consult  Gray's 
Absolute  Measurements  in  Electricity  and  Magnetism, 
Kempe's  Electrical  Measurement,  or  Ayrton's  Practical 
Electricity. 

448.  Measurement  of  Electromotive-Force.  —  There  be- 
ing no  easy  absolute  method  of  measuring  electromotive- 
forces,  they  are  usually  measured  relatively,  by  comparison 
with  the  electromotive-force  of  a  standard  cell,  such  as 
Clark's  or  the  Weston  normal  cell  (Art.  201).  The  methods 
of  comparison  are  various ;  only  five  are  here  mentioned. 

(a)  Reduced  Deflexion  Method.  —  Call  the  electromotive- 
force  of  the  battery  to  be  measured  E,  and  E'  that  of  a 
standard  battery.     Join  E  with  a  galvanometer,  and  let  it 
produce  a  deflexion  of  §1  degrees  through  the  resistances  of 
the  circuit ;    then  add  enough  resistance  r  to  bring  down  the 
deflexion  to  S2  degrees  —  say  10  degrees  less  than  before. 
Now  substitute  the  standard  battery  in  the  circuit  and  ad- 
just the  resistances  till  the  deflexion  is  Si  as  before,  and  then 
add  enough  resistance  r'  to  bring  down  the  deflexion  to  B2. 

Then 

r' :  r  =  E' :  E, 

since  the  resistances  that  will  reduce  the  strength  of  the 
current  equally  will  be  proportional  to  the  electromotive- 
forces.  (Not  recommended.) 

(b)  Potentiometer  Method.  —  If  the  poles  of  a  constant 
battery  are  joined  by  a  long  thin  wire,  the  potential  will 
fall  uniformly  from  the  +  to  the  —  pole.     Hence,  by  making 
contacts  at  one  pole  and  at  a  point  any  desired  distance 
along  the  wire,  any  desired  proportional  part  of  the  whole 


CH.  vi.  448]         MEASUREMENT   OF   FORCE  427 

electromotive-force  can  be  taken.  This  proportional  part 
may  be  balanced  against  the  electromotive-force  of  any 
cell  as  follows :  —  Let  a  uniform  thin  wire  of  platinoid  or 
german-silver  be  stretched  over  a  scale  divided  into  say 
2000  parts.  Connect  a  Clark  standard  cell  LC  through  a 
sensitive  galvanometer,  as  shown  in  Fig.  252,  to  make  con- 
tact at  the  1434  division  of  the  scale.  Then  connect  a 
single  accumulator  cell  B,  or  two  Daniells,  with  a  sliding 


Fia.  252.  —  Diagram  of  Potentiometer. 

contact,  as  shown,  and  move  it  up  and  down  until  a  point  is 
found  such  that  the  galvanometer  shows  that  the  Clark  cell 
is  balanced.  Then  connect  the  cell  X  whose  E.M.F.  is  to 
be  measured,  and  slide  its  contact  along  the  wire  until  it  also 
is  balanced.  Suppose  it  balances  at  1024  of  the  scale,  its 
E.M.F.  will  be  1-024.  A  single  galvanometer  will  suffice 
if  the  wire  to  X  is  joined  in  between  G  and  the  Clark  cell. 

(c)  Voltmeter  Method.  —  If   a  galvanometer  be  used  so 
that  the  resistance  of  its  circuit  is  several  thousand  ohms 
(in  comparison  with  which  the  internal  resistance  of  a  bat- 
tery or  dynamo  machine  is  insignificant),  it  will  serve  as  a 
voltmeter  to  measure  electromotive-forces ;    for  the  strength 
of  current  through  it  will  depend  only  on  the  electromotive- 
force  between  the  ends  of  the  coil.     (See  Art.  237  on  Volt- 
meters.) 

(d)  Condenser  Method.  —  A  condenser  of  known  capacity 
is  charged  from  a  standard  cell,  and  then  discharged  through 
a  ballistic  galvanometer  (Art.  234).     The  cell  to  be  compared 
is  then  substituted  for  the  standard  cell.     The  E.M.F.  is 
proportional  to  the  throw  of  the  galvanometer. 


428  ELECTRICITY   AND   MAGNETISM     [PT.  n.  449 

(e)  Electrometer  Method.  —  The  electromotive-force  of  a 
battery  may  be  measured  directly  as  a  difference  of  poten- 
tials by  a  quadrant  electrometer  (Art.  307).  In  this  case  the 
circuit  is  never  closed,  and  no  current  flows. 

449.  Measurement  of  Internal  Resistance  of  Cells.  — 
This  may  be  done  in  several  ways. 

(a)  Condenser  Method.  —  As  in  (d)  of  preceding  Article, 
observe  throw  of  galvanometer  from  condenser  charged  by 
the  cell.     Then  shunt  the  cell  with  a  suitably  high  resist- 
ance R  and  take  another  charge  and  discharge.     If  the  two 
throws  are  called  di  and  d2,  the  internal  resistance  will  be 
=  R(di  -  dj/d* 

(b)  Half-deflexion  Method.  —  Place  the  cell  in  series  with 
a  galvanometer  the  resistance  of  which  is  G,  and  a  resistance- 
box  in  which  there  is  unplugged  a  resistance  R  such  that  the 
deflexion  is  conveniently  large.     Now  increase  the  resistance 
in  the  box  until  it  is  seen  by  the  deflexion  that  the  current 
has  been  reduced  to  half  what  it  was.     If  this  added  resist- 
ance is  called  a,  then  by  Ohm's  law  it  follows  that  the  internal 
resistance  is  =  a  —  (R  -f  G).     This  method  is  suitable  for 
very  high  internal  resistances. 

(c)  Method  of  Opposition.  —  Take  two  similar  cells  and 
join  them  in  opposition  to  one  another,  so  that  they  send  no 
current  of  their  own.     Then  measure  their  united  resistance 
just  as  the  resistance  of  a  wire  is  measured.     The  resistance 
of  one  cell  will  be  half  that  of  the  two. 

(d)  Mance's  Method.  —  Place  the  cell  itself  in  one  arm 
of  the  Wheatstone's  bridge,  and  put  a  key  where  the  battery 
usually  is,  adjust  the  resistances  till  the  permanent  galva- 
nometer deflexion  is  the  same  whether  the  key  be  depressed 
or  not.     When  this  condition  of  things  is  attained  the  battery 
resistance  is  balanced  by  those  of  the  other  three  arms.     ( Not 
a  reliable  method.) 

(e)  Alternating    Current    Method.  —  If    greater    accuracy 
is  required  in  the  opposition  method,  the  cells  in  opposi- 
tion may  be  placed  in  one  of  the  arms  of  a  Wheatstone's 


CH.  vi.  450]     MEASUREMENT   OF    RESISTANCE 


429 


bridge  in  which  instead  of  the  usual  battery  is  inserted  the 
secondary  coil  of  a  small  induction  coil  (without  condenser), 
while  a  telephone  receiver  is  used  instead  of  a  galvanometer. 
The  ceasing  of  the  buzzing  in  the  telephone  corresponds  to 
null  deflexion. 

450.  Measurement  of  Resistance  of  Electrolytes.  — 
Electrolytes  have  a  true  resistance  which  is  found  to  remain 
constant  when  measured  with  currents  of  different  strength, 
provided  the  back  electromotive-forces  at  the  electrodes,  due 
to  polarization  (Art.  183),  are  eliminated.  Kohlrausch 
modified  Wheatstone's  bridge  for  this  service,  by  applying 
alternating  currents,  and  substituting  a  telephone  receiver 
(Art.  593)  for  the  galvanometer.  The  bridge  is  adjusted  until 
the  sound  in  the  telephone  is  a  minimum.  The  usual  form  of 
apparatus  is  shown  diagrammatically  in  Fig.  253. 

This  method  may  be  modified  by  the  use  of  Whetham's 
commutator  which  renders  it  more  rapid  and  more  accurate. 
A  continuous  current  is  led 
to  an  ebonite  drum  turned  by 
a  motor  or  a  hand  wheel.  On 
the  drum  are  fixed  brass  strips 
with  wire  brushes  touching 
them  in  such  a  manner  that 
the  current  is  reversed  several 
times  in  each  revolution.  The 
wires  from  the  drum  are  con- 
nected with  the  ends  of  the 
wire  bridge.  A  moving  coil  galvanometer  (whose  coil  pos- 
sesses a  high  moment  of  inertia)  is  used  as  indicator,  and  on 
the  other  end  of  the  drum  is  another  set  of  strips  arranged  to 
reverse  periodically  the  galvanometer  connexions,  so  that 
any  residual  current  flows  through  it  continuously  and  not 
alternating.  These  strips  are  slightly  narrower  than  the 
first;  set  thus  the  galvanometer  circuit  is  made  just  after 
and  broken  just  before  the  battery  circuit.  When  the 
measured  resistance  is  not  altered  by  increasing  the  speed  of 


FIG.  253.  —  Kohlrausch's  Bridge. 


430  ELECTRICITY   AND   MAGNETISM     [PT.  n.  451 

the  commutator,  or  changing  the  ratio  of  the  arms  of  the 
bridge,  the  disturbing  effects  may  be  considered  to  be 
eliminated. 

In  this  way  a  measurement  is  obtained  of  the  resistance 
of  the  column  of  liquid  between  the  electrodes  of  the  cell. 
To  calculate  the  conductivity  of  the  liquid  the  area  of  the 
electrodes  and  their  distance  apart  must  be  observed.  As 
the  temperature  coefficient  of  conductivity  is  large  (2  %  per 
degree)  it  is  advisable  to  place  the  resistance  cell  in  a  water 
bath  and  to  observe  its  temperature  with  some  accuracy. 

451.  Measurement  of  Capacity.  —  The  capacity  of  a  con- 
denser may  be  measured  by  comparing  it  with  the  capacity 
of  a  standard  condenser  —  such  as  the  J  microfarad  con- 
denser (Fig.  174)  —  in  one  of  the  following  ways  :  — 

(a)  Electrometer  Method.  —  Charge  the  condenser  of  un- 
known capacity  to  a  certain  potential  ;    then  make  it  share 
its  charge  with  the  condenser  of  known  capacity,  and  meas- 
ure the  potential  to  which  the  charge  sinks  ;    then  calculate 
the  original  capacity,  which  will  bear  the  same  ratio  to  the 
joint  capacity  of  the  two  as  the  final  potential  bears  to  the 
original  potential. 

(b)  Ballistic  Galvanometer   Method.  —  Charge    each    con- 
denser to  equal  differences  of  potential  from  the  same  cell  or 
battery,  and  then  discharge  each  successively  through  a  ballis- 
tic galvanometer  (Art.  234).     The  throw  of  the  needle  will  be 
proportional  in  each  case  to  the  charge,  and  therefore  to  the 
capacity. 

The  law  of  the  ballistic  galvanometer  is  :  — 


, 

G        7T 

where  Q  is  the  quantity  of  electricity  (in  C.G.S.  units),  C  the 
capacity  of  the  condenser,  V  the  volts  applied,  H  the  magnetic 
field,  G  the  constant  of  the  galvanometer,  T  the  period  of  one 
complete  swing  of  the  needle,  and  a  the  angle  of  first  throw.  The 
factor  H/G  may  be  eliminated  by  passing  a  continuous  current  i 


CH.  vi.  451]      MEASUREMENT   OF   CAPACITY 


431 


to  produce  a  steady  deflexion  /3  ;  when 

i  =  —  tan  /8. 
G 

Combining  this  with  the  preceding,  we  have 


If  a  and  /3  are  both  small  this  becomes 
Q  =  iTa/2  •*$  ; 

where  if  i  is  in  amperes,  Q  will  be  in  coulombs. 

For  a  d'Arsonval  galvanometer,  when  used  ballistically, 

Q  =  Ti  +  2  ir, 

where  T  =  one  period,  and  i  is  the  steady  current  which  produces 
a  deflexion  equal  to  the  throw. 

(c)  Bridge    Method.  —  Connect    the    two    condensers    Ci 
and  €2  in  two  arms  of  a  Wheatstone's  bridge  and  adjust  the 
resistances  so  that  there  is  no  de- 

flexion on  charge  or  discharge 
(Fig.  254).  Then  Ci  :  C2  :  :  r2  :  n, 
the  larger  capacity  acting  as  a 
smaller  resistance. 

(d)  Potential-divider  Null  Method. 
-Two  resistances  r\  and  r2   are 

joined  in  series  to  the  +  and  — 
poles  of  a  battery.  The  middle 
point  between  r\  and  r2  is  con- 
nected to  one  of  the  terminals  of  Ci  and  also  of  C2.  The  free 
terminals  of  Ci  and  C2  are  momentarily  joined  to  the  +  and  — 
poles  of  the  battery  respectively  and  receive  charges  of  oppo- 
site sign.  They  are  then  connected  ;  and  if  of  equal  amount 
the  charges  will  neutralize  each  other.  The  resistances  r\ 
and  r2  are  adjusted  until  this  condition  is  satisfied,  as  shown 
by  null  deflexion  when  the  key  of  a  galvanometer  circuit 
across  their  terminals  is  depressed.  Then  Ci  :  C2  :  :  rz  :  r\. 

(e)  Tuning-fork    Method.  —  A    tuning-fork    acting    as    a 
vibrating  two-way  switch  charges  and  discharges  the  con- 


FIG.  254.  —  Comparison  of  Capa- 
cities by  Bridge  Method. 


432         ELECTRICITY   AND   MAGNETISM     [PT.  n.  452,  453 


denser  n  times  per  second,  allowing  to  pass  VCn  coulombs 
per  second  or  VCn  amperes.  The  apparent  resistance  r 
of  this  combination  is  1/Cn,  and  can  be  measured  by  a 
Wheatstone  bridge,  whence  C  =  1/nr. 

(/)  Loss  of  Charge  Method.  —  This  is  the  same  as  the 
last  method  in  Art.  443e,  a  known  high  resistance  being  used. 
452.    Measurement   of   Resistance   by  Amperemeter   and 
Voltmeter.  —  If  an  amperemeter  is  used  to  measure  the  am- 
peres going  through  any  conductor,  and  at  the  same  time  a 

voltmeter  is  used 
"   to  measure  the  dif- 
ference of  potential 
between  its   ends, 
then  the  resistance 
—  of  that  conductor 
(assuming   that 


Lamps 


FIG.  255.  —  Measurement  of  Resistance  by  Amperemete 
and  Voltmeter. 


there  are  no  elec- 
tromotive-forces 
being  generated  in 
it)  can  be  found  by 
dividing  the  volts  by  the  amperes ;  since  R  =  E  -s-  i.  This 
method  can  be  used,  for  example,  to  find  the  resistance  of  a 
glow-lamp  while  it  is  alight.  Or  it  may  be  used  (Fig.  255) 
to  ascertain  the  resistance  of  a  whole  circuit  of  lamps. 

453.  Ohmmeter.  —  The  Ohmmeter  is  an  instrument  to 
read  the  ratio  which  the  volts  applied  to  a  conductor  bear 
to  the  current  thereby  produced  in  it ;  that  ratio  being  read 
off  direct  on  the  scale.  The  instrument  (which  usually  also 
contains  a  small  generator  to  provide  a  current)  is  a  species 
of  galvanometer  so  arranged  that  the  amperes  pass  through 
a  fixed  coil,  and  the  current  proportional  to  the  volts  passes 
through  a  second  fixed  coil  at  right  angles  to  the  first.  A 
suitably  pivoted  needle  takes  up  a  diagonal  position  at  an 
angle  the  tangent  of  which  is  proportional  to  the  ratio  of 
volts  to  amperes,  and  may  therefore  be  graduated  to  read 
ohms.  In  the  Ohmmeters  employed  for  testing  high  resist- 


CH.  vi.  454]  MEASUREMENT  OF  ELECTRIC  ENERGY  433 

ances  such  as  a  megohm  or  more,  an  electromotive-force  of 
500  volts  is  usually  generated. 


LESSON  XXXV.  —  Electric  Energy  and  Measurement 

454.  Electric  Energy.  —  An  electric  current  conveys 
energy  from  a  battery  or  dynamo  to  some  other  part  of  the 
circuit,  where  it  is  transformed  back  into  work  —  mechanical, 
chemical,  or  thermal  work.  We  must  inquire  into  this  elec- 
trical energy  and  into  the  rate  at  which  it  is  generated  or 
utilized. 

Power  is  the  rate  at  which  energy  is  being  received  or 
spent.  It  may  be  expressed  in  foot-pounds  per  second,  or  in 
ergs  per  second,  or  in  watts,  or  in  kilowatts.  James  Watt  con- 
sidered a  horse  capable  on  the  average  of  working  at  the  rate 
of  550  foot-pounds  per  second  (against  gravity).  Since  1 
foot  =  3048  centimetres,  and  the  force  of  1  Ib.  (=  453-6 
grammes  X  981)  =  445,000  dynes,  nearly,  it  follows  that 
1  horse-power  is  equivalent  to  7,460,000,000  (or  746  X  107) 
ergs  per  second. 

If  a  quantity  of  electricity  Q  is  moved  through  a  differ- 
ence of  potential  V,  it  follows  from  the  definition  (Art.  280) 
that  the  work  done  is  equal  to  QV.  If  this  is  occurring  in  a 
battery  or  dynamo,  QV  represents  electrically  the  work 
(chemical  or  mechanical)  done  on  the  system,  or  the  energy 
received  (electrically)  by  the  system.  Now,  suppose  this 
operation  to  have  occupied  time  t,  the  rate  at  which  the  energy 
is  being  imparted  to  the  circuit  will  be  QV/£.  But  (Art.  169) 
Q/Z  =  i.  Hence  the  power  given  to  the  circuit  is  equal  to  iV. 

This  justifies  the  statement  that  the  power  of  an  electric 
current  to  perform  useful  work,  whether  in  lighting,  heating, 
or  producing  mechanic  actions,  is  proportional  both  to  the 
strength  of  the  current  and  to  the  electromotive-force  which 
drives  it.  In  other  words,  power  is  proportional  to  both  am- 
peres and  volts  jointly.  [Similarly  the  power  of  a  steam  en- 
gine is  proportional  not  only  to  the  quantity  of  steam  it  uses 
2r 


434  ELECTRICITY   AND   MAGNETISM      [PT.  n.  455 

per  second,  but  also  to  the  pressure  at  which  the  steam  is 
supplied.]  The  electric  unit  of  power  will  then  be  the  power 
of  a  current  of  1  ampere  driven  by  an  electric  pressure  of  1 
volt.  This  unit  is  known  as  1  watt. 

To  find  the  number  of  watts  of  power  supplied  by  any 
dynamo  or  battery,  multiply  the  number  of  amperes  of 
current  by  the  number  of  volts  at  which  the  current  is  driven. 
The  same  rule  serves  to  calculate  the  power  electrically  de- 
livered to  any  motor,  lamp,  accumulator,  or  other  means  of 
spending  electric  energy. 

Since  1  volt  =  10 8  absolute  units  of  E.M.F.,  and  1  ampere 
=  10 -1  absolute  units  of  current  (Art.  381),  it  follows  that  1 
watt  =  10 7  absolute  units  of  power  (i.e.  10 7  ergs  per  second). 
But  1  horse-power  =  746  X  10 7  ergs  per  second  (see  above). 
Hence  1  H.P.  =  746  watts. 

Horse-power  =  i  X  V  -f-  746. 

Example.  —  If  a  current  of  20  amperes  is  supplied  to  an  arc- 
lamp  at  a  pressure  of  56  volts,  find  the  amount  of  power 
absorbed  therein.  Ans.  1120  watts  or  1|  H.P. 

One  thousand  watts  is  called  1  kilowatt.  The  kilowatt  is 
therefore  approximately  1J  H.P. 

Kilowatts  =  i  X  V  -h  1000. 

The  reader  is  warned  that  in  the  case  of  alternating 
currents,  if  there  is  any  difference  of  phase  between  the 
volts  and  the  amperes,  the  true  power  (watts)  will  be  less 
than  the  volt-amperes,  for  in  such  cases  the  power-factor 
(Art.  531)  must  also  be  taken  into  account. 

455.  Input  and  Output.  —  Any  generator  of  electric  power, 
such  as  a  dynamo,  battery,  or  thermopile,  when  connected 
to  a  circuit  to  which  it  supplies  the  electric  power,  is  giving  an 
output,  which  may  be  expressed  in  watts  or  kilowatts.  It 
also  is  receiving  from  some  source,  mechanical,  chemical,  or 
thermal,  an  input  of  power.  Any  motor,  electric  lamp, 
electroplating  cell,  or  heater,  which  is  supplied  electric  power 


CH.  vi.  456]  EFFICIENCY  435 

through  a  circuit  is  said  to  be  receiving  electrically  an  input 
which  may  likewise  be  expressed  in  watts  or  kilowatts  and 
which  is  being  converted  into  mechanical,  luminous,  chemical, 
or  thermal  energy.  Thus  a  dynamo  supplying  300  amperes 
at  a  potential  difference  of  200  volts  between  its  terminals 
is  said  to  be  giving  an  output  l  of  60  kilowatts  ;  and  a  motor 
taking  80  amperes  from  mains  at  500  volts  is  said  to  have  an 
input  of  40  kilowatts.  The  question  whether  the  machine 
through  which  a  current  is  flowing  is  giving  out  or  taking  in 
electric  power  depends  on  the  question  (Art.  264)  whether 
the  machine  is  generating  an  electromotive  force  which  helps 
the  current  (as  in  dynamos)  or  opposes  2  it  (as  in  motors). 

456.  Efficiency.  —  The  name  of  the  efficiency  is  given  to  the 
ratio  between  output  and  input.  In  a  dynamo  the  input 
is  mechanical,  being  the  power  given  (by  the  engine)  me- 
chanically to  the  driving  shaft  ;  and  the  output  is  electrical, 
being  the  power  delivered  to  the  circuit,  as  measured  at  the 
terminals  of  the  machine.  Both  quantities  must,  of  course, 
be  expressed  in  the  same  units  ;  both  in  watts,  or  both  in  kilo- 
watts. In  a  motor  the  input  is  electrical,  and  the  output 
mechanical  ;  the  latter  being  the  power  delivered  at  the  shaft 
of  the  machine.  The  difference  between  the  output  and  the 
input  is  the  power  that  is  lost. 

We  may  write  it  thus  :  — 

efficiency  = 


input      output  +  losses 

1  The  word  output,  as  applied  to  central  station  work  is  sometimes  used 
in  the  sense  of  total  outflow  of  amperes  irrespective  of  voltage,  but  this 
should  rather  be  called  the  load. 

2  Consider  the  mechanical  analogue  of  transmission  of  power  from  one 
pulley  to  another  pulley  by  a  belt.     The  effort  in  the  driving  pulley  is  in  the 
same  direction  as  the  motion  of  the  belt.     The  effort  in  the  driven  pulley 
is  opposed  in  direction  to  the  motion.     (See  also  Art.  264.) 

This  fundamental  principle  accounts  for  the  back-electromotive-forces 
observed  in  motors,  and  in  accumulators  while  being  charged.  Because 
of  it  we  know  (Art.  174)  that  the  seat  of  the  main  electromotive-force  in  a 
voltaic  cell  is  at  the  surface  of  the  zinc,  and  that  (Art.  474)  bismuth  is 
thermo-electrically  positive  to  antimony. 


436        ELECTRICITY   AND   MAGNETISM     [FT.  n.  457,  458 


Example,  —  Suppose  a  dynamo  generates  736  amperes  at  250 
volts  between  its  terminals,  and  that  it  takes  270  H.P. 
as  measured  at  the  shaft.  The  output  is  250  X  736  = 
184000  watts  =  184  kilowatts.  The  input  is  270  X  746 
=  201420  watts  =  201*42  kilowatts.  The  efficiency  is 
184000  -5-  201420  =  0'9134,  or  91-34  per  cent.  The 
losses  amount  to  201420  -  184000  =  17420  watts  =  1712 
kilowatts. 

457.    Power-Measurement.  —  To  measure  the  power  given 

electrically  to  any  part  ab  of  a  circuit  by  an  unvarying  cur- 
rent, it  suffices  to  measure  the  current 
with  an  amperemeter  (Art.  238),  and 
the  potentials  across  the  part  with  a 
voltmeter  (Arts.  237,  309),  the  latter 
being  of  course  connected  as  a  shunt 
as  in  Fig.  256.  Then,  if  the  current 
is  unvarying,  the  product  of  volts  and 
amperes  gives  the  watts.  Or  a  watt- 
meter may  be  used  as  below. 

458.    Wattmeters.  —  The  product  of 

amperes  and  volts  may  be  measured  directly  by  means  of  a 

wqttmeter.      This  name  is  given  to  a  variety  of  electrody- 

namometer  (Art.  425)  in  which  the 

fixed  and   movable   coils   constitute 

two   separate   circuits,  one  being  a 

thick  wire  of  low  resistance  to  carry 

the  amperes,  the  other  being,  or  in- 
cluding, a  thin  wire  of  high  resistance 

(as  in  voltmeters)  to  receive  a  current 

proportional  to  the  volts.     The  latter 

circuit  is  to  be  connected  as  a  shunt 

to  the  part  ab  of  the  circuit  in  which 

the  supplied  power  is  to  be  measured. 

256,  the  part  ab  is  an  arc-lamp. 


FIG.  256.  —  Measurement  of 
Power  by  Amperemeter 
and  Voltmeter. 


a 

1 

jmf 

r 

arc?/ 

£ 

IT 

\ 

$--'. 

n> 

-v-  _ 

IW 


FIG.  257.  —  Measurement  of 
Power  by  Wattmeter. 


In  Fig.  257,  as  in  Fig. 
The  auxiliary  resistance  r 
is  introduced  into  the  thin-wire  circuit  of  the  instrument,  the 
whole  current  flowing  through  the  thick-wire  circuit. 

Wattmeters  are  made  both  on  the  pattern  of  Siemens's 


CH.  vi.  459,  460]    ELECTRIC   SUPPLY   METERS  437 

dynamometer  (Art.  426)  and  on  that  of  Kelvin's  balances 
(Art.  427). 

When  power-measurements  have  to  be  made  on  alternate- 
current  circuits,  separate  instruments  must  not  be  used,  as 
in  Art.  457,  to  measure  volts  and  amperes.  For,  owing  to 
the  differences  of  phase  (Art.  524)  between  voltage  and  cur- 
rent, the  apparent  watts,  or  volt-amperes,  calculated  by  mul- 
tiplying the  separate  readings,  will  be  in  excess  of  the  true 
watts  as  measured  by  a  wattmeter. 

459.  Power  wasted  in  Heating.  —  If  a  current  i  is  driven 
through  a  resistance  R,  the  volts  needed  will  (by  Ohm's  law) 

be  V  =  iR. 

The  power  iV  so  expended  will  merely  heat  the  resistance. 
Substitute  for  V  its  value  as  above,  and  we  have 

Watts  wasted  =  iV  =  PR  =  V2/R. 

Or,  if  the  expenditure  goes  on  for  t  seconds,  the  amount 
of  energy  turned  into  heat  (joules)  will  be 

Energy  =  QV  =  itV  =  i2Rt  (see  Art.  462). 

The  nett  power  of  a  dynamo  or  battery  is  always  less 
than  its  gross  power,  because  of  internal  resistance.  If  r 
be  the  internal  resistance,  and  E  the  whole  electromotive- 
force,  the  nett  or  available  volts  V  =  E  -  ir.  The  gross 
power  will  be  ~E,i  watts.  But  the  nett  power  will  be 
Vi  =  Ei  -  &r.  Or,  the  available  watts  equal  the  total 
watts  generated,  less  the  watts  wasted  in  internal  heating. 

460.  Supply  Meters.  —  Meters  for  measuring  the  supply 
to  the  houses  of  consumers  are  of  several  kinds. 

(a)  Chemical  Meters.  —  The  current  or  a  known  fraction 
of  it  is  passed  through  an  electrolytic  cell,  there  to 
deposit  copper  or  dissolve  zinc.  The  amount  of 
chemical  action  is  proportional  to  the  ampere-hours. 
In  another  type  two  electrodes  dip  into  an  electrolyte 
such  as  acidulated  water.  The  decomposition  of  the 


438 


ELECTRICITY  AND   MAGNETISM      [FT.  n.  460 


electrolyte  lowers  the  solution,  and  the  lowering  is  a 
measure  of  the  ampere-hours. 

(6)  Motor  Meters.  —  If  the  current  passes  through  the 
armature  of  a  small  motor  (Art.  516)  having  a  con- 


0  }  Counting  Gear 


FIG.  258.  —  Elihu  Thomson  Supply  Meter. 

stant  field,  and  having  its  speed  controlled  purely  by 
eddy-current  friction  (Art.  500),  in  an  aluminium  disk 
revolving  between  magnet  poles,  its  speed  will  at 
every  instant  be  proportional  to  the  current.  Hence 
such  a  motor  attached  to  a  suitable  counting-train 
of  wheels  will  serve  as  a  meter,  the  total  number  of 
revolutions  being  proportional  to  the  ampere-hours. 
In  Perry's  meter  the  revolving  part  is  a  copper  bell 
immersed  in  mercury,  revolving  around  a  central 
magnet  pole  (as  the  wire  does  in  Fig.  234),  and  sur- 
rounded by  an  external  S-pole  with  ribbed  projections 


CH.  vi.  460]         ELECTRIC   SUPPLY   METERS  439 

to  promote  eddy  currents.  In  Ferranti's  meter  the 
mercury,  lying  as  a  horizontal  circular  pool,  through 
which  the  current  flows  radially  in  a  vertical  magnetic 
field,  rotates  and  moves  the  registering  wheels  in 
proportion  to  the  current  that  passes  through.  In 
Elihu  Thomson's  motor  meter  (Fig.  258),  which  re- 
cords the  watt-hours,  the  revolving  armature  A  is 
of  fine  wire  and  high  resistance,  connected  as  shunt, 
while  the  fixed  coils  F  that  serve  as  field-magnet 
take  the  whole  current  supplied.  So  the  torque  is 
proportional  to  the  watts ;  while  an  aluminium  disk 
D  revolving  between  magnet  poles  M,  by  its  drag 
(Art.  500)  acts  as  a  brake  and  keeps  the  speed  propor- 
tional to  the  torque.  To  compensate  for  inevitable 
friction  of  the  pivots,  it  is  arranged  to  provide  a  small 
auxiliary  field  by  means  of  an  additional  coil  S  which 
is  connected  into  the  shunt  circuit.  A  good  meter 
should  start  turning  when  the  current  going  to  the 
lamps  is  less  than  1  per  cent  of  the  normal  load. 

(c)  Retarded    Clocks.  —  Current    may    be    made    to    act 
upon  the  rate  of  a  clock,  by  flowing  in  a  coil  under 
the  pendulum  bob  if  the  latter  is  a  magnet.     Any 
force  added  thus  to  gravity  or  subtracted  from  it  will 
cause  the  clock  to  gain  or  lose.     Ayrton  and  Perry 
proposed  to  measure  the  supply  by  the  total  time 
gained  or  lost  by  a  clock.     In  Aron's  meter,  of  which 
this  is  the  principle,  there  is  a  double  clock  with  two 
pendulums,  only  one  of  which  is  acted  on  by  the 
current.     A  train  of  counting  wheels  is  geared  to  re- 
cord the  difference  between  the  two. 

(d)  Integrating      Meters.  —  A       uniformly-going      clock 
drives  a  counting  apparatus  through  an  intermediate 
gear  operated  by  the  current  (or  by  the  watts),  this 
intermediate  gear  being  such  that  when  current  is 
small  the  counting  is  small ;  when  current  is  large  the 
counting    is    large.     An    integrating    disk-and-roller, 


440  ELECTRICITY  AND   MAGNETISM      [PT.  n.  460 

or  an  integrating  cam,  is  a  usual  mechanism,  its  opera- 
tion being  controlled  by  the  motion  of  an  ampere- 
meter or  wattmeter. 

(e)  Alternating  Current  Meters.  —  For  measuring  the  con- 
sumption on  an  alternating  supply,  the  motor  in  the 
meter  must  be  one  of  such  a  type  as  is  suitable  for  al- 
ternating currents.  In  practice  there  is  used  a  simple 
form  of  induction  motor  (Art.  549),  in  which  the 
rotor  is  a  simple  aluminium  disk,  and  the  stator  is  re- 
placed by  a  laminated  electromagnet  having  a  split- 
pole  winding,  so  as  to  create  the  difference  of  phase 
necessary  to  procure  rotation.  The  same  disk,  so 
driven,  may  at  the  same  time  serve  also  as  the  eddy- 
current  brake  (Art.  500),  turning  between  the  poles 
of  a  permanent  magnet. 


CHAPTER  VII 

ELECTRIC    PRODUCTION   OF  HEAT 

LESSON  XXXVI.  —  Heating  Effect  of  Currents 

461.  Heat  and  Resistance.  —  A  current  may  do  work 
of  various  kinds,  chemical,  magnetic,  mechanical,  and  ther- 
mal. In  every  case  where  a  current  does  work  that  work 
is  done  by  the  expenditure  of  part  of  the  energy  that  is  being 
supplied  to  the  circuit.  We  have  seen  that,  by  the  law  of 
Ohm,  the  current  produced  by  a  given  battery  is  dimin- 
ished in  strength  by  anything  that  increases  the  external 
resistance.  But  the  current  may  be  diminished,  in  certain 
cases,  by  another  cause,  namely,  the  setting  up  of  an  oppos- 
ing electromotive-force  at  some  point  of  the  circuit.  Thus,  in 
passing  a  current  through  an  electrolytic  cell  (Art.  252)  there 
is  a  diminution  due  to  the  opposing  electromotive-force  ("  po- 
larization ")  which  is  generated  while  the  chemical  work  is 
being  done.  So,  again,  when  a  current  is  used  to  drive  an  elec- 
tric motor  (Art.  455),  the  rotation  of  the  motor  will  itself 
generate  a  back  E.M.F.,  which  will  diminish  the  current. 
Whatever  energy  is,  however,  not  expended  in  this  way  in  doing 
work  against  a  back  electromotive-force  is  frittered  down  into 
heat,  either  in  the  generator  or  in  some  part  of  the  circuit,  or 
in  both.  Suppose  a  quantity  of  electricity  to  be  set  flowing 
round  a  closed  circuit.  If  there  were  no  resistance  to  stop 
it  it  would  circulate  for  ever;  just  as, a  waggon  sent  rolling 
along  a  circular  railway  should  go  round  for  ever  if.  it  were 
not  stopped  by  friction.  When  matter  in  motion  is  stopped 
by  friction  the  energy  of  its  motion  is  frittered  down  by 
the  friction  into  heat.  When  electricity  in  motion  is  stopped 
by  resistance  the  energy  of  its  flow  is  frittered  down  by 

441 


442 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  462 


the  resistance  into  heat.  Heat,  in  fact,  appears  wherever 
the  circuit  offers  a  resistance  to  the  current.  If  the  terminals 
of  a  battery  be  joined  by  a  short  thick  wire  of  small  resist- 
ance, most  of  the  heat  will  be  developed  in  the  battery  and 
so  wasted ;  whereas,  if  a  thin  wire  of  relatively  considerable 
resistance  be  interposed  in  the  outer  circuit,  it  will  grow  hot, 
while  the  battery  itself  will  remain  compara- 
tively cool. 

462.  Laws  of  Development  of  Heat :  Joule's 
Law.  —  To  investigate  the  development  of 
heat  by  a  current,  Joule  and  Lenz  used  instru- 
ments on  the  principle  shown  in  Fig.  259.  A 
thin  wire  joined  to  two  stout  conductors  is  en- 
closed within  a  glass  vessel  containing  water, 
into  which  also  a  thermometer  dips.  The 
resistance  of  the  wire  being  known,  its  relation 
to  the  other  resistances  can  be  calculated. 
Joule  found  that  the  number  of  units  of  heat 
developed  in  a  conductor  is  proportional  — 
(i.)  to  its  resistance ; 
(ii.)  to  the  square  l  of  the  strength  of  the 

current ;  and 

(iii.)  to  the  time  that  the  current  lasts. 
The    equation    expressing   these   relations   is    known    as 
Joule's  Law,  and  is  — 

U  =  i2m  XO-24, 

where  i  is  the  current  in  amperes,  R  the  resistance  in  ohms, 
t  the  time  in  seconds,  and  U  the  heat  in  calories ;  one  calorie 

1  The  second  of  the  above  laws,  that  the  heat  is,  cceteris  paribus,  pro- 
portional to  the  square  of  the  strength  of  the  current,  often  puzzles  students, 
who  expect  the  heat  to  be  proportional  to  the  current  simply.  Such  may 
remember  that  the  consumption  of  zinc  is,  cceteris  paribus,  also  proportional 
to  the  square  of  the  current ;  for,  suppose  that  in  working  through  a  high 
resistance  (so  as  to  get  all  the  heat  developed  outside  the  battery)  we  double 
the  current  by  doubling  the  number  of  battery  cells  in  series,  there  will 
be  twice  as  much  zinc  consumed  as  before  in  each  cell,  and  as  there  are 
twice  as  many  cells  as  at  first  the  consumption  of  zinc  is  four  times  as  great 
as  before. 


FIG.  259.  —  Water 
heated  by  Elec- 
tric Current. 


CH.  vii.  463]  JOULE'S   LAW  443 

being  the  amount  of  heat  that  will  raise  1  gramme  of  water 
through  1°  C.  of  temperature  (Art.  299). 

This  equation  is  equivalent  to  the  statement  that  a  current 
of  one  ampere  flowing  through  a  resistance  of  one  ohm  develops 
therein  0-24  calorie  per  second.  The  heat  produced  thus  by 
the  degradation  of  energy  in  a  resistance  is  sometimes  called 
the  "  ohmic  "  heat  to  distinguish  it  from  the  heat  of  the  re- 
versible Peltier  effect  (Art.  472).  The  mechanical  equivalent 
of  heat  (Joule's  equivalent),  is  42  million  ergs  to  1  calorie; 
so  W  =  JU,  where  W  is  the  work  in  ergs,  U  the  heat  in 
calories,  and  J  =  4-2  X  107.  Hence  U  =  i2Rt/J.  But  to 
reduce  to  ergs  we  must  multiply  i2Ht  by  107 ;  whence  U 
=  &Rt  X  0-24. 

The  number  0-24,  which  appears  above,  arises  in  the 
following  way :  The  product  i'2R  is  the  number  of  watts 
(Art.  454) ;  and  i2Rt  is  the  number  of  watt-seconds,  or  joules 
(Art.  381)  or  units  of  energy  expended  as  heat  in  the  resist- 
ance. Experimentally  it  is  found  that  the  ordinary  heat- 
unit  or  calorie  is  equal  to  4-2  joules ;  or  1  joule  is  equal  to  0*24 
calorie. 

463.  Favre's  Experiments.  —  Favre,  repeating  Joule's  re- 
searches, made  a  series  of  most  important  experiments  on  the 
relation  of  the  energy  of  a  current  to  the  heat  it  develops.  He 
ascertained  that  the  number  of  calories  evolved  when  33  grammes 
(1  equivalent)  of  zinc  are  dissolved  in  dilute  sulphuric  acid  (from 
which  it  causes  hydrogen  to  be  given  off)  is  18,682.  This  figure 
was  arrived  at  by  conducting  the  operation  in  a  vessel  placed  in  a 
cavity  of  his  calorimeter,  an  instrument  resembling  a  gigantic 
thermometer  filled  with  mercury,  the  expansion  of  which  was 
proportional  to  the  heat  imparted  to  it.  When  a  Smee's  cell  was 
introduced  into  the  same  instrument,  the  solution  of  the  same 
amount  of  zinc  was  observed  to  be  accompanied  by  the  evolution 
of  18,647  calories  (i.e.  an  amount  almost  identical  with  that 
observed  before),  and  this  amount  was  the  same  whether  the 
evolution  took  place  in  the  battery-cell  when  the  circuit  was  closed 
with  a  short  thick  wire,  or  whether  it  took  place  in  a  long  thin  wire 
placed  in  the  external  circuit.  He  then  arranged  5  Smee's  cells  in 
series,  in  cavities  of  the  calorimeter,  and  sent  their  current  round  a 


444  ELECTRICITY   AND   MAGNETISM     [PT.  n.  464 

small  electric  motor.  The  amount  of  heat  evolved  during  the 
solution  of  33  grammes  of  zinc  was  then  observed  in  three  cases: 
(i.)  when  the  motor  was  at  rest ;  (ii.)  when  the  motor  was  running 
round  and  doing  no  work  beyond  overcoming  the  friction  of  its 
pivots;  (iii.)  when  the  motor  was  employed  in  doing  13,124,000 
gramme-centimetres  ( =  12,874  X  186  ergs}  of  work,  by  raising  a 
weight  by  a  cord  running  over  a  pulley.  The  amounts  of  heat 
evolved  in  the  circuit  in  the  three  cases  were  respectively,  18,667, 
18,657,  and  18,374  calories.  In  the  last  case  the  work  done  ac- 
counts for  the  diminution  in  the  heat  wasted  in  the  circuit.  If 
we  add  the  heat-equivalent  of  the  work  done  to  the  heat  evolved 
in  the  latter  case,  we  ought  to  get  the  same  value  as  before.  Divid- 
ing the  12,874  X  186  ergs  of  work  by  Joule's  equivalent  (42  X  106), 
we  get  as  the  heat-equivalent  of  the  work  done  306  calories.  Now 
18,374  +  306  =  18,680,  a  quantity  which  is  almost  identical 
with  that  of  the  first  observation,  and  quite  within  the  limits  of 
unavoidable  experimental  error. 

464.  Rise  of  Temperature.  —  The  elevation  of  tempera- 
ture in  a  resisting  wire  depends  on  the  nature  of  the  resistance. 
A  very  short  length  of  a  very  thin  wire  may  be  found  which 
has  the  same  resistance  as  a  long  length  of  stout  wire.  Each 
will  cause  the  same  number  of  units  of  heat  to  be  evolved, 
but  in  the  former  case,  as  the  heat  is  spent  in  warming  a  short 
thin  wire  of  small  mass,  it  will  get  very  hot,  whereas  in  the 
latter  case  it  will  perhaps  only  warm  to  an  imperceptible 
degree  the  mass  of  the  long  thick  wire;  which,  moreover, 
has  a  larger  surface  to  get  rid  of  its  heat.  If  the  wire  weigh 
w  grammes,  and  have  a  specific  capacity  for  heat  s,  then 
U  =swO,  where  0  is  the  rise  of  temperature  in  deg.  C.  Hence 
if  none  of  the  heat  were  radiated  away 

0  =  0-24  X— - 

sw 

Since  the  resistance  of  metals  increases  as  they  rise  in 
temperature,  a  thin  wire  heated  by  the  current  will  resist 
more,  and  grow  hotter  and  hotter  until  its  rate  of  loss  of 
heat  by  conduction  and  radiation  into  the  surrounding  air 
equals  the  rate  at  which  heat  is  supplied  by  the  current. 


CH.  vii.  464]  RISE   OF   TEMPERATURE  445 

The  following  pretty  experiment  illustrates  the  laws  of 
heating.  The  current  from  a  few  cells  is  sent  through  a 
chain  made  of  alternate  pieces  (Fig.  260  a)  of  copper  C  and 
iron  F  wires  of  equal  gauge.  The  iron  links  glow  red-hot 
while  the  copper  links  remain  comparatively  cool.  The 
explanation  is  that  the  resistivity  of  iron  is  about  seven 
times  that  of  copper,  and  its  capacity  for  heat  about  three- 
quarters  as  great;  hence 
the  rise  of  temperature  in  *  "^^»g_  F 
wires  of  equal  thickness 

traversed    by    the    same     — „, 

current   is    roughly   nine  r|  c[  F|  c|   F|  c|   F|  c[    b 

times  as  great  for  iron  as  I,    I     I     I     I     I     I  i  l^,^ 

for  CODDer  FIG.  260.  —  Wire  Links  heated  —  a  in  Series, 

-,,..*,  i  6  m  Parallel. 

Thin  wires  heat  much 

more  rapidly  than  thick  ones  carrying  the  same  current ;  the 
rise  of  temperature  in  different  parts  of  the  same  wire  (carrying 
the  same  current)  would  be,  for  different  thicknesses,  inversely 
proportional  to  the  fourth  power  of  the  diameters  if  they  had 
equal  surfaces  for  radiation. 

Thus,  suppose  a  wire  at  any  part  to  have  been  reduced 
to  half  its  diameter,  the  cross-section  will  have  an  area 
|  as  great  as  in  the  thicker  part.  The  resistance  here  will 
be  4  times  as  great,  and  the  number  of  heat  units  developed 
will  be  4  times  as  great  as  in  an  equal  length  of  the  thicker 
wire.  But  4  times  the  amount  of  heat  spent  on  \  the  amount 
of  metal  would  warm  it  to  a  degree  16  times  as  great :  and 
the  thin  wire  has  only  half  as  much  surface  for  getting  rid  of 
heat.  But  the  hotter  a  body  becomes  the  more  freely  does 
it  radiate  heat  to  things  around  it.  For  wires  of  given  mate- 
rial, the  current  needed  to  raise  them  to  an  equal  temperature 
varies  as  the  square  root  of  the  cube  of  the  diameter.  This 
law  applies  to  the  sizes  of  wires  used  as  safety-fuses  in  electric 
lighting.  These  are  pieces  of  tin  wire  interposed  in  the 
circuit  to  melt  if  by  any  chance  the  current  becomes  abnor- 
mally strong. 


446 


ELECTRICITY  AND   MAGNETISM       [PT.  n.  465 


If  supplied  at  the  same  voltage,  thin  wires  heat  less  than 
thick  ones  of  the  same  length  and  material ;  for  they  offer 
a  greater  resistance,  and  therefore  less  current  flows  through 
them.  For  this  case  it  is  convenient  to  state  Joule's  law  in 
another  form.  Since  iR  =  V,  and  i2  =  V2  -f-  R2,  the  sub- 
stitution of  this  in  the  formula  of  Art.  462  gives  us 

U  =  0-24  X  V2*  -i-  R. 

The  heat  developed  in  a  resistance  R  at  a  constant  voltage 

V  is  inversely  proportional  to  the  resistance. 

If  a  grid  is  made  of  a  number  of  iron  and  copper  wires  of 

equal  length  and  thickness  arranged  in  parallel,  as  in  Fig. 

260  6,  and  a  strong  current  is  sent  through  them,  the  copper 

links  will  heat  while  the  iron  ones  remain  cool. 

465.    Hot-wire      Instruments.  —  The      current      flowing 

through  a  long  thin  platinum  wire  of  high  resistance,  when 
it  is  made  to  connect  two  points  on 
a  circuit,  will  measure  the  potential 
difference  between  these  two  points. 
Owing  to  the  wire  becoming  warmed 
it  will  expand ;  and  its  expansion 
may  be  made  to  move  a  hand  over 
a  dial  graduated  to  read  volts  (Fig. 


FIG.  261.  —  Cardew's  Hot-wire 
Voltmeter. 


FIG.  262.  —  Hot-wire  Ampere- 
meter. 


261) ;  and  it  becomes  a  hot-wire  voltmeter.  Fig.  262  depicts 
the  arrangements  in  a  modern  hot-wire  amperemeter.  The 
current  to  be  measured  passes  through  a  horizontally 


CH.  vii.  466-468]     BLASTING   AND  WELDING  447 

stretched  fine  wire,  which  is  pulled  downwards  by  a  second 
wire  that  is  itself  stretched  sideways  by  a  spring  S,  by  means 
of  a  fine  thread  passing  around  a  small  roller.  When  a  cur- 
rent passes  through  the  fine  wire  it  heats  it,  causing  it  to 
expand  slightly.  As  the  spring  pulls  it  down  through  the 
second  wire  it  turns  the  roller  and  moves  an  indicating  hand 
over  a  scale.  The  scale  is  graduated  by  finding  experiment- 
ally the  points  to  which  the  hand  turns  when  1  ampere,  2 
amperes,  etc.,  are  passed  through  the  instrument.  Hot-wire 
instruments  are  specially  applicable  for  measuring  alternat- 
ing currents,  since  a  wire  heats  whichever  way  the  current 
flows  along  it. 

466.  Electric    Cautery.  —  For   surgical    purposes   a   thin 
platinum  wire,  heated  red-hot  by  a  current,  is  sometimes 
used  instead  of  a  knife,  as,  for  example,  in  the  operation  of 
amputating  the  tongue  for  cancer.     Platinum  is  chosen  on 
account  of  its  infusibility,  but  even  platinum  wires  are  fused 
by  the  current  if  too  strong. 

467.  Blasting  by  Electricity.  —  In  consequence  of  these 
heating  effects,  electricity  can  be  applied  in  blasting  and  min- 
ing to  ignite  the  charges.     Stout  conducting  wires  are  carried 
from  an  appropriate  battery  at  a  distance  to  a  special  fuse, 
in  which  a  very  thin  platinum  wire  is  joined  in  the  circuit. 
This  wire  becomes  hot  when  the  current  ^flows ;    and  being 
laid  amidst  an  easily  combustible  substance  to  serve  as  a 
priming,  ignites  this  and  sets  fire  to  the  charge  of  gunpowder. 
Submarine  mines  are  thus  exploded  beneath  the  water,  and 
at  any  desired  distance  from  the  battery. 

468.  Electric  Welding.  —  If  two  wires  or  rods  of  metal 
are  held  together  with  sufficient  force  while  a  very  large 
current  is  passed  through  them,  much  heat  is  developed  at 
the  junction,  so  that  they  soften  and  become  welded  together. 
The  processes  of  electric  welding  have  been  perfected  by  Elihu 
Thomson,   who  has  utilized  for  this  purpose  alternating- 
current  transformers  (Art.  538)  to  produce  currents  of  many 
hundred  amperes  at  a  pressure  of  a  few  volts. 


448  ELECTRICITY  AND   MAGNETISM    [PT.  n.  469,  470 

A  singular  effect  is  noticed  when  two  iron  rods  connected 
to  the  two  poles  of  a  powerful  source  at  50  or  more  volts 
are  dipped  into  water.  The  rod  which  serves  as  kathode  is 
observed  to  be  covered  with  a  luminous  layer,  and  it  presently 
becomes  red-hot.  Guthrie,  who  first  investigated  this  phe- 
nomenon in  1876,  ascribed  the  heating  to  the  resistance  of  a 
film  of  hydrogen.  This  effect  has  been  made  the  basis  of  a 
welding  method. 

469.  Electric  Furnaces.  —  Electric  furnaces  are  of  three 
kinds :     (i.)  resistance  furnaces,  in  which  a  current  is  sent 
through  a  special  resistance  of  platinum,  nickel,  or  other 
refractory  wire,  to  act  as  a  heater ;  (ii.)  arc  furnaces,  in  which 
an  electric  arc  is  caused  to  play  inside  a  crucible  to  melt  the 
contents ;     (iii.)  induction  furnaces,  in  which  a  current  is 
produced,  in  the  material  to  be  melted,  inductively,  that  is 
by  a  species  of  transformer  action  (see  Art.  538).     By  these 
means  higher  temperatures  can  be  attained  than  those  in 
ordinary  combustion  furnaces ;  moreover  the  furnace  is  more 
compact,  more  efficient,  and  free  from  ordinary  products  of 
combustion. 

Electric  furnaces  are  now  largely  used  for  steel-refining, 
for  the  manufacture  of  aluminium,  calcium  carbide,  carbo- 
rundum ;  and  for  hardening  steel  tools.  Also  for  the  produc- 
tion of  nitrates  from  the  nitrogen  of  the  atmosphere.  See 
Art.  529. 

470.  Electric    Cooking.  —  Since   public   supplies   of   elec- 
tricity became  common,  electric  stoves,  ovens,  and  heaters 
for  cooking,  stewing,  etc.,  have  become  articles  of  commerce. 
The  heating  is  effected  by  passing  currents  through  resist- 
ance-wires embedded  in  cement  or  other  suitable  insulating 
material.     These  wires  are  usually  of  nickel,  or  of  an  alloy 
called  nichrome  containing  nickel  and  chromium.     Electric 
cooking  probably  does  not  pay,  as  compared  with  the  use 
of  fuels,  if  the  price  charged  for  electric  energy  exceeds  one 
penny   per   unit.     But    there    are    obvious    advantages    in 
cleanliness  and  avoidance  of  products  of  combustion. 


CH.  vii.  471, 472]  PELTIER  EFFECT  449 

LESSON  XXXVII.  —  Thermo-Eledric  Currents 

471.  Seebeck  Effect.  —  In  1821  Seebeck  discovered  that 
a  current  may  be  produced  in  a  closed  circuit  by  heating  a 
point  of  contact  of  two  dissimilar  metals.     If  a  piece  of  bis- 
muth and  a  piece  of  antimony  be  soldered  together,  and  their 
free  ends  connected  with  a  short-coil  galvanometer,  it  is  found 
that  if  the  junction  be  warmed  to  a  temperature  higher  than 
that  of  the  rest  of  the  circuit,  a  current  flows  in  the  direction 
from  bismuth  to  antimony  across  the  heated  point,  the  cur- 
rent   being    proportional    to    the    excess    of    temperature. 
If  the  junction  is  cooled  below  the  temperature  of  the  rest  of 
the  circuit  a  current  in  the  opposite  direction  is  observed. 
The  electromotive-force  thus  set  up  will  maintain  the  current 
so  long  as  the  excess  of  temperature  of  the  heated  point  is 
kept  up ;   heat  being  all  the  while  absorbed  in  order  to  main- 
tain the  energy  of  the  current.     Such  currents  are  called 
Thermo-electric  currents,  and  the  electromotive-force  pro- 
ducing them  is  known  as  Thermo-electromotive-force. 

472.  Peltier  Effect.  —  In  1834  Peltier  discovered  a  phe- 
nomenon which  is  the  converse  of  that  discovered  by  Seebeck. 
He  found  that  if  a  current  of  electricity  from  a  battery  be 
passed  through  a  junction  of  dissimilar  metals  the  junction 
is  either  heated  or  cooled,  according  to  the  direction  of  the 
current.     Thus  a  current  which  passes  through  a  bismuth- 
antimony  pair  in  the  direction  from  bismuth  to  antimony 
absorbs  heat  in  passing  the  junction  of  these  metals,  and  cools 
it ;    whereas,  if  the  current  flow  from  antimony  to  bismuth 
across  the  junction  it  evolves  heat,  and  the  junction  rises  in 
temperature.     It  is  clear  that  if  bismuth  is  positive  with  re- 
spect to  antimony,  any  current  that  may  be  caused  to  flow 
from  bismuth  to  antimony  is  aided  by  the  electromotive 
force  at  that  junction ;  whilst  any  current  flowing  from  anti- 
mony to  bismuth  will  meet  with  an  opposing  electromotive- 
force.     In  the  latter  case  the  current  will  do  work  and  heat  the 
junction ;  in  the  former  the  current  will  receive  energy  at  the 

2a 


450  ELECTRICITY   AND   MAGNETISM         [PT.  n.  472 

expense  of  the  junction,  which  will  give  up  heat.  In  Fig.  263, 
the  feathered  arrows  at  the  junctions  represent  the  Peltier 
electromotive-forces,  and  the  plain  arrows  the  direction  of 
the  current. 

This  phenomenon  of  heating  (or  cooling)  by  a  current, 
where  it  crosses  the  junction  of  two  dissimilar  metals  (known 
as  the  "  Peltier  effect,"  to  distinguish  it  from  the  ordinary 
heating  of  a  circuit  where  it  offers  a  resistance  to  the  current, 


FIQ.  263.  —  Diagram  of  Peltier  Effect. 

which  is  sometimes  called  the  "  Joule  effect  "),  is  utterly 
different  from  the  evolution  of  heat  in  a  conductor  of  high 
resistance,  for  (a)  the  Peltier  effect  is  reversible ;  the  current 
heating  or  cooling  the  junction  according  to  its  direction, 
whereas  a  current  meeting  with  resistance  in  a  thin  wire  heats 
it,  whichever  be  the  direction  it  flows ;  and  (6)  the  amount 
of  heat  evolved  or  absorbed  in  the  Peltier  effect  is  propor- 
tional simply  to  the  current,  not  to  the  square  of  the  current 
as  the  heat  of  resistance  is. 

The  complete  law  of  the  heat  developed  in  a  circuit  will 
therefore  require  to  take  into  account  any  Peltier  effects 
which  may  exist  at  metal  junctions  in  the  circuit.  If  the 
letter  P  stand  for  the  difference  of  potential  due  to  the  heat- 
ing of  the  junction,  expressed  as  a  fraction  of  a  volt,  then  the 
complete  law  of  heat  is 

U  =  0-24  X(i2Rt  ±  Pit), 

which  the  student  should  compare  with  Joule's  law  in  Art. 
462.  The  quantity  called  P  is  also  known  as  the  coefficient 
of  the  Peltier  effect ;  it  has  different  values  for  different  pairs 
of  metals,  and  is  numerically  equal  to  the  number  of  ergs  of 
work  which  are  evolved  as  heat  at  a  junction  of  the  particular 
metals  by  the  passage  of  one  absolute  unit  (10  coulombs) 


CH.  vii.  473,  474]    THERMO-ELECTRIC   POWER  451 

of  electricity  through  the  junction.  The  reversible  heat 
alone  =  ±  0-24  X  Pit. 

473.  Thermo-electric  Laws.  —  The  thermo-electric  prop- 
erties of  a  circuit  are  best  studied  by  reference  to  the  simple 
circuit  of  Fig.  264,  which 

represents  a  bismuth- 
antimony  pair  united  by  a 
copper  wire.  If  all  parts 
of  the  circuit  are  at  one 
temperature,  even  though 
there  may  be  at  the  junc- 
tions electromotive-forces 
as  suggested  above,  there 

FIG.  264.  —  Simple  Thermo-electric  Couple. 

will  be  no  current,  since 

the  electromotive-forces  are  in  equilibrium.  But  when  a 
junction  is  heated  this  equilibrium  no  longer  exists,  and  there 
will  be  a  resultant  electromotive-force.  It  is  found  to  obey 
the  following  laws  :  — 

(i.)  The  thermo-electromotive-force  is,  for  the  same  pair 
of  metals,  proportional  (through  limited  ranges  of 
temperature)  to  the  excess  of  temperature  of  the  junc- 
tion over  the  rest  of  the  circuit. 

(ii.)  The  total  thermo-electromotive-force  in  a  circuit  is  the 
algebraic  sum  of  all  the  separate  thermo-electromotive- 
forces  in  the  various  parts. 

It  follows  from  this  law  that  the  various  metals  can  be 
arranged,  as  Seebeck  found,  in  a  series,  according  to  their 
thermo-electric  power,  each  one  in  the  series  being  thermo- 
electrically  positive  (as  bismuth  is  to  antimony)  toward  one 
lower  down. 

474.  Thermo-electric    Power.  —  In    the    following    table 
is  shown  the  thermo-electric  series  of  metals,  together  with  the 
thermo-electric  power  of  each  when  cold.     The  term  thermo- 
electric power  of  a  metal  means  the  electromotive  force  per 
degree  (centig.)  for  a  pair  made  of  that  metal  with  the  stand- 


452  ELECTRICITY  AND  MAGNETISM      [PT.  n.  475 

ard  metal  (lead).     In  the  table  the  numbers  are  microvolts 
per  degree. 

+  Bismuth 89  to  97 

Nickel 22 

German-silver       .         .         .         .  11*75 

Lead  0 

Platinum  - -     CH) 

Copper -     1-36 

Zinc      .         .         .         .         .         .  -     2'3 

Iron —  17'5 

Antimony     .         .         .         .         .  -  22'6  to  -26'4 

Tellurium -  502 

-  Selenium -  800 

A  very  small  amount  of  impurity  may  make  a  great  dif- 
ference in  the  thermo-electric  power  of  a  metal ;  and  some 
alloys,  and  some  of  the  metallic  sulphides,  as  galena,  exhibit 
extreme  thermo-electric  properties. 

The  electromotive-forces  due  to  heating  single  pairs  of 
metals  are  very  small  indeed.  If  the  junction  of  a  copper 
iron  pair  be  raised  1°  C.  above  the  rest  of  the  circuit  its  elec- 
tromotive-force is  only  16-14  microvolts.  That  of  the  more 
powerful  bismuth-antimony  pair  is  for  1°  C.,  about  117 
microvolts.  Thermo-electric  power  varies,  however,  with 
temperature:  for  example,  that  of  iron  is  really  —  17-5  -}- 
0-049  t  (where  t  is  the  mean  temperature  of  the  two  junctions), 
iron  becoming  less  negative  when  hot.  Copper  is  —  1-36 
—  0-01  t,  becoming  more  negative.  There  will  be  obviously 
one  particular  temperature  or  neutral  point,  at  which  the 
powers  of  iron  and  copper  will  be  equal. 

475.  Thermo-electric  Inversion.  —  Gumming  discovered 
that  in  the  case  of  iron  and  other  metals  an  inversion  of 
their  thermo-electric  properties  may  take  place  at  a  high 
temperature.  In  the  case  of  the  copper-iron  pair  the  tem- 
perature of  275°  is  a  neutral  point ;  below  that  temperature 
the  current  flows  through  the  hotter  junction  from  the  copper 
to  the  iron ;  but  when  the  circuit  is  above  that  temperature 
iron  is  thermo-electrically  positive  to  copper.  The  neutral 


CH.  vii.  476]     THERMO-ELECTRIC   DIAGRAM 


453 


point  for  a  zinc-iron  pair  is  about  200°.  The  inversion  is 
easily  shown  by  heating  the  junction  of  two  long  strips  of 
these  metals,  riveted  together  in  a  V-form,  and  watching  the 
effect  on  a  galvanometer  connected  to  their  other  ends. 
There  will  at  first  be  a  deflexion  which  will  go  on  increasing 
until  the  temperature  of  200°  is  attained,  but  on  further  heat- 
ing the  junction  the  deflexion  diminishes  and  at  about  400° 
reverses,  the  current  flowing  the 
other  way.  Fig.  265  shows  graph- 
ically the  curves  obtained  with 
iron-zinc  and  iron-copper  pairs 
when  one  junction  is  kept  at  0° 
while  the  other  is  heated.  The 
dotted  line  is  for  the  iron-zinc 
pair  when  one  junction  is  kept  at 
50°  and  the  other  heated. 

476.    Thermo-electric   Diagram.  —  The  facts    of   thermo- 
electricity are  best  studied  by  means  of  the  diagrams  sug- 


0°          100°       200°      300°      400°  C 

FIG.  265.  —  Diagram  of  Thermo- 
electric Inversion. 


FIG.  266.  —  Diagram  of  Thermo-electric  Electromotive  Forces. 

gested  by  Lord  Kelvin  and  constructed  by  Professor  Tait. 
In  that  given  in  Fig.  266  the  horizontal  divisions  represent 


454  ELECTRICITY   AND   MAGNETISM      [PT.  n.  476 

the  temperatures;  the  vertical  distances  indicating  the 
thermo-electric  power,  in  microvolts  per  degree.  These 
powers  are  measured  with  respect  to  the  metal  lead,  which 
is  taken  as  the  standard  of  zero  at  all  temperatures,  because, 
while  with  other  metals  there  appears  to  be  a  difference  of 
potentials  between  the  metal  hot  and  the  same  metal  cold, 
hot  lead  brought  into  contact  with  cold  lead  shows  no  per- 
ceptible thermo-electric  difference. 

An  example  will  illustrate  the  usefulness  of  the  diagram. 
Let  a  circuit  be  made  by  uniting  at  both  ends  a  piece  of  iron 
and  a  piece  of  zinc ;  and  let  the  two  junctions  be  kept  at  0° 
and  100°  respectively  by  melting  ice  and  boiling  water.  Then 
the  total  electromotive-force  round  the  circuit  is  represented 
by  the  area  a,  0,  —  15,  b.  The  slope  of  the  lines  for  the 
various  metals  represents  the  property  referred  to  above,  of 
an  electromotive-force  between  differently-heated  portions 
of  the  same  metal  accompanied  by  an  absorption  or  evolu- 
tion of  heat  when  the  current  flows  from  a  hotter  to  a  colder 
portion  of  the  same  metal.  This  effect,  known  as  the  Thom- 
son effect  from  its  discoverer  Sir  W.  Thomson  (Lord  Kelvin), 
is  opposite  in  iron  to  what  it  is  in  copper  or  zinc.  Copper 
when  hot  is  negative  compared  with  copper  that  is  cold. 
Hence  if  a  current  is  sent  from  a  hot  to  a  cold  part  of  a  piece 
of  copper  it  encounters  an  opposing  electromotive-force. 
Hence  when  a  current  of  electricity  flows  from  a  hot  to  a  cold 
point  in  copper  it  evolves  heat ;  and  it  absorbs  heat  when  it 
flows  from  a  cold  point  to  a  hot  point  in  the  copper.  In  iron 
a  current  flowing  from  a  hot  point  to  a  cold  point  absorbs 
heat. 

The  thermo-electromotive-force  of  a  pair,  of  which  the 
junctions  are  at  temperatures  T  and  t  respectively,  and  of 
which  n  is  the  temperature  of  the  neutral  point,  may  be 
conveniently  expressed  by  the  following  formula : 


CH.  vii.  477] 


THERMO-ELECTRIC   PILES 


455 


where  p  is  the  volts  per  degree  (at  0°)  as  given  in  the  table 
(Art.  474). 

477.  Thermo-electric  Piles.  —  The  electromotive-force 
of  a  bismuth-antimony  pair,  when  the  junctions  are  kept 
at  0°  and  100°,  is  only  0-0115  volt.  In  order  to  increase  the 
electromotive-force  of  thermo-electric  pairs  it  is  usual  to  join 
a  number  of  pairs  of  metals  (preferably  bismuth  and  anti- 
mony) in  series,  but  so  bent 
that  the  alternate  junctions  can 
be  heated  as  shown  in  Fig.  267 
at  BBB,  whilst  the  other  set 
AAA  are  kept  cool.  The  vari- 
ous electromotive-forces  then 
all  act  in  the  same  direction, 
and  the  current  is  increased  in 
proportion  to  the  number  of 
pairs  of  junctions.  Powerful 
thermo-electric  batteries  have 
been  made  by  Clamond,  Noe, 
and  others.  Such  batteries 
have  been  made  of  groups  of 
pairs  of  iron  and  an  alloy  of  zinc  with  antimony,  arranged 
around  a  small  furnace ;  but  it  is  extremely  difficult  to  main- 
tain them  in  effective  action  for  long,  as  they  fail  after  con- 
tinued use,  probably  owing  to  a  permanent  molecular  change 
at  the  junctions.  In  the  hands  of  Melloni  the  thermo-electric 
pile  or  thermopile,  constructed  of  many  small  pairs  of  anti- 
mony and  bismuth  united  in  a  compact  form,  proved  an  ex- 
cellent electrical  thermometer  when  used  in  conjunction  with 
a  sensitive  short-coil  astatic  galvanometer.  For  the  detec- 
tion of  excessively  small  differences  of  temperature  the 
thermopile  is  an  invaluable  instrument,  the  currents  being 
proportional  to  the  difference  of  temperature  between  the 
hotter  set  of  junctions  on  one  face  of  the  thermopile  and  the 
cooler  set  on  the  other  face.  The  arrangement  of  a  thermo- 
pile with  the  old  astatic  galvanometer  is  shown  in  Fig.  268. 


FIG.  267.  —  Battery  of  Three  Thermo- 
electric Pairs. 


456 


ELECTRICITY   AND   MAGNETISM         [PT.  n.  478 


A  thermopile  devised  by  Rubens,  which  has  a  small  thermal 
capacity,  and  therefore  is  quick  in  its  action,  consists  of  a 


FIG.  268.  —  Nobili's  Thermopile  with  Astatic:  Galvanometer. 

number   of  junctions  of  iron  and  constantan  wires.      The 
E.M.F.  generated  is  53  microvolts  per  centigrade  degree  per 
couple.     The  junctions  are  arranged  in  a 
IP        BjP  zigzag  form  (Fig.    269),   so   that   the   al- 

|°|  |°|  ternate  junctions  are  in  a  vertical  straight 
line ;  the  remaining  junctions  being  half  to 
one  side  and  half  to  the  other  side,  thus 
escaping  being  heated.  This  arrangement 
of  the  working  junctions  in  a  vertical  line 
is  very  convenient  for  the  examination  of 
the  heat-spectrum. 

478.  Thermo-galvanometers.  —  A  still 
more  sensitive  arrangement  for  detecting 
minute  heating  due  to  radiation  consists 
in  suspending  between  the  poles  of  a  powerful  magnet  a 
closed  circuit  having  a  bismuth-antimony  junction  in  it. 
Sturgeon  proposed  such  a  thermo-galvanometer  in  1835. 


FIG.  269.  —  Rubens's 
Thermopile. 


CH.  vii.  479,  480] 


PYROMETERS 


457 


\Mirrer 


FIG.   270.  —  Boys's   Radio- 
micrometer. 


In  the  radio-micrometer  of  Vernon  Boys  (1889)  a  loop  of 
silver  wire,  suspended  by  a  delicate  quartz  fibre  between  the 
poles  of  a  magnet  (Fig.  270),  has  its  cir- 
cuit closed  at  its  lower  end  by  a  piece  of 
antimony  and  a  piece  of  bismuth  (or 
alloys  of  these  metals)  soldered  to  a 
minute  disk  of  copper  foil.  A  rise  of 
temperature  of  the  copper  foil  even  so 
small  as  one  millionth  of  a  degree  will 
generate  a  current  in  the  loop  and  give 
a  deflexion  over  one  division  of  the  scale. 
With  an  instrument  of  this  kind  the 
radiant  heat  of  a  candle  can  be  detected 
at  a  distance  of  two  miles. 

DuddelPs  thermo-galvanometer  con- 
sists of  an  arrangement  like  Fig.  270,  with  the  addition  of  a 
small  heater  (a  platinum  resistance)  through  which  is  carried 
the  current  to  be  measured.  The  deflexions  are  approxi- 
mately proportional  to  the  heat  developed  in  the  heater.  A 
current  of  half  a  microampere  can  thus  be  detected. 

479.  Thermal  Cross.  —  Fig.  271  depicts  an  arrangement, 
useful  for  measuring  small  alternating  currents,  in  which 
two  wires  of  metals  such  as  iron  and  nickel  are  twisted  into 

a  junction  J  ;  two  ends,  a,  b,  of 
the  cross  being  joined  to  a  galva- 
nometer G  ;  the  other  two  ends, 
a',  &',  going  to  an  external  circuit. 
Any  current  passing  along  this  ex- 
ternal circuit  heats  the  junction, 
evoking  there  a  thermo-electro- 
motive-force  and  deflecting  the 

galvanometer 

480.  Thermo-electric    Pyrometers.  —  For   measuring  the 
temperatures  of  furnaces  Le  Chatelier  devised  an  electric 
pyrometer  (Fig.  272),  consisting  of  a  pair  of  highly  infusible 
wires,  one  of  platinum,  the  other  of  a  rhodio-platinum  alloy, 


FI0.  m.  -  Thermo-e,ec,nc  Cross. 


458 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  480 


united  at  a  junction  that  can  be  introduced  into  a  furnace. 
They  are  enclosed  in  a  tube  of  porcelain.  The  other  ends 
of  the  wires  are  connected  to  a  suitable  galvanometer  or 


FIG.  272.  —  Thermo-electric  Pyrometer. 

millivoltmeter,  which  may  be  calibrated  directly  so  as  to 
read  the  furnace  temperatures  direct  in  centigrade  degrees. 
In  Foster's  pyrometer  the  couple  is  made  of  two  alloys  of 
chromium  and  nickel  in  different  proportions. 

1  For  other  appliances  of  electric  thermometry,  see  Darling's  Pyrometry. 


CHAPTER  VIII 

ELECTRIC    LIGHT 

LESSON  XXXVIII.  —  Glow-lamps 

481.  Development  of  the  Glow-lamp.  —  Glow-lamps  con- 
sist of  a  thin  wire  or  filament  of  some  infusible  conductor, 
enclosed  in  a  glass  bulb,  and  heated  to  whiteness  by  the 
current.     Thin  wires  of  platinum  or  iridium  were  often  sug- 
gested, but  could  not  be  kept  from  fusing.     Edison  in  1878 
devised  a  lamp  consisting  of  a  platinum  spiral  combined  with 
a  short-circuiting  switch  to  divert  the  current  from  the  lamp 
in   case   it   became   overheated.     Swan   in   February    1879 
publicly  showed  a  carbon  wire   lamp   in  a  vacuous   bulb. 
Edison  in  October  1879  devised  a  vacuum  lamp  with  a  coiled 
filament  made  of  lamp  black  and  tar  carbonized.     Swan  in 
January  1880  prepared  filaments  from  cotton  thread  parch- 
mentized    in    sulphuric    acid,    and    afterwards    carbonized. 
Edison  in  1880  substituted  a  flat  strip  of  carbonized  bamboo 
for  a  filament. 

For  twenty  years  the  carbon  glow-lamp  held  the  market, 
to  be  superseded  by  new  kinds  having  metallic  filaments. 
First,  Auer  von  Welsbach  (1898)  employed  wires  of  osmium, 
followed  by  von  Bolton  (1903)  using  tantalum,  and  by  Just 
and  Kuzel  (1904-5)  using  tungsten.  Whatever  the  material, 
it  must  be  exceedingly  refractory,  it  must  have  a  high 
electric  resistance,  and  it  must  be  capable  of  being  fashioned 
into  a  wire  not  much  thicker  than  a  hair. 

482.  Carbon   Glow-lamps.  —  Carbon   glow-lamps  mostly 
have  fine  carbon  wires  prepared  from  threads  of  parch- 
mentized  cellulose,  which  are  then  carbonized  in  a  closed 

459 


460  ELECTRICITY  AND   MAGNETISM       [PT.  n.  482 

vessel.  Sometimes  the  filaments  are  "  flashed  "  over  with 
surface  carbon  by  being  momentarily  heated  electrically  in 
a  carbonaceous  atmosphere.  They  are  mounted  upon  sup- 
ports in  a  glass  bulb  through  which  leading-in  wires  pass 
out,  and  into  which  they  are  sealed ;  the  bulbs  being  after- 
wards exhausted  of  air  and  other  gases.  The  vacuum  is 
made  very  perfect  by  the  employment  of  special  mercurial 
air-pumps.  The  bulbs  should  be  heated  during  exhaustion 
to  drive  out  residual  gases.  Two 
early  forms  of  glow-lamp  are  shown  in 
Fig.  273 :  the  form  used  by  Swan  in 
England,  and  that  perfected  by  Edison 
in  America.  The  resistance  of  such 
lamps  varies  according  to  size  and 
length  of  the  filament.  A  16  candle- 
power  carbon  lamp  for  use  on  a  100- 

FlG'  2?3'  ^mpsb°n  GI°W"    volt  circuit  wil1  take  about  0-6  ampere. 
That  is  to  say,  its  resistance  when  hot 

will  be  about  166  ohms,  or  over  200  ohms  when  cold,  since 
carbon  has  the  property  of  offering  a  lower  resistance  when 
hot  than  when  cold,  the  reverse  of  that  observed  in  metals. 
It  will  absorb  about  60  watts.  This  is  at  the  rate  of  less 
than  4  watts  per  candle.  Used  so,  it  will  last  on  the  average 
over  1000  hours  of  burning.  Lamps  are  made  to  give  equal 
light  and  use  less  current,  by  using  a  thinner  and  rather 
shorter  filament ;  but  then  they  do  not  last  so  long.  The 
surface  disintegrates  in  time  if  forced  to  emit  too  much 
light.  The  power  required  to  operate  12  such  60-watt  lamps 
will  be  720  watts,  or  nearly  1  horse-power. 

The  light  increases  as  about  the  sixth  power  of  the  volts ; 
the  energy  consumed  is  only  as  the  second  power.  But 
raising  the  volts  a  little,  shortens  the  life  enormously :  an 
increase  of  only  6  per  cent  reduces  the  life  to  about  one- 
third  of  the  normal  value.  The  temperature  attained  is 
usually  under  2000°  C.  These  lamps  deteriorate  with  use ; 
the  candle-power  going  down  after  1000  hours'  use  by  some 


CH.  viii.  483]  GLOW-LAMPS  461 

25  or  30  per  cent.  Though  carbon  is  practically  infusible, 
carbon  glow-lamps  must  not  be  supplied  with  too  much 
current ;  for,  when  overrun,  though  they  give  more  light  for 
the  time  they  speedily  perish  owing  to  a  disintegration  of  the 
glowing  surface. 

Glow-lamps  are  usually  grouped  in  parallel  (see  Art.  558 
and  Fig.  330)  between  mains  kept  at  constant  voltage.  The 
usual  voltages  employed  are  100  to  110  volts,  and  200  to 
220  volts.  For  higher  voltages  the  thinness  of  the  filaments 
renders  them  undesirable.  Little  fairy-lamps  of  1  to  8 
candle-power,  with  short  filaments  for  lighting  by  batteries, 
work  at  from  1J  to  10  volts. 

483.  Metallic  Glow-lamps.  —  The  temperature  of  fusion 
of  most  metals  is  below  a  white  heat.  Amongst  the  highest 
are  platinum  1755°  C. ;  titanium  1900° ;  irid- 
ium  2300° ;  osmium  2700° ;  tantalum  2850° ; 
tungsten  3000°.  Most  of  these  are  not  only 
refractory  but  very  hard  ;  and  there  are  great 
mechanical  difficulties  in  drawing  them  into 
wires.  Osmium,  tantalum,  and  tungsten  have 
all  been  used  with  success ;  but  osmium  is  too 
dear  for  commercial  use.  Tungsten  can  now 
be  drawn  into  wires  of  extreme  tensity  and 
strength  and  has  come  into  general  use  for 
glow-lamps.  But  when  glowing  it  readily 
combines  with  oxygen :  hence  in  tungsten  FIG.  274.  —  Me- 
lamps  care  must  be  taken  that  the  bulbs 
shall  be  most  perfectly  exhausted  of  air. 
The  fine  wires  are  stretched  in  zigzags  upon  an  interior 
frame  as  seen  in  Fig.  274,  which  represents  one  of  the 
glow-lamps  of  the  Osram  Company.  Owing  to  the  high 
resistance  and  the  very  high  temperature  which  tungsten 
can  withstand,  the  tungsten  lamps  are  very  efficient,  par- 
ticularly those  of  large  candle-power,  in  which  during 
their  life  the  efficiency  may  attain  the  value  of  1}  candles 
per  watt. 


462          ELECTRICITY  AND   MAGNETISM     [PT.  n.  484,  485 


The  following  table  gives  some  data  about  a  60-watt, 
100- volt  tungsten  lamp  if  used  at  different  voltages : 


VOLTS 

AMPERES 

WATTS 

CANDLE- 
POWER 

WATTS  PER 
CANDLE 

PROBABLE 
LIFE  (HOURS) 

90 

0-565 

51 

31 

1-65 

8400 

95 

0'58 

55 

38 

1'45 

3250 

100 

0*60 

60 

48 

1/25 

1200 

105 

0'62 

65 

55 

no 

540 

110 

0-635 

70 

70 

i-oo 

280 

The  circumstance  that  the  resistance  of  the  metals  rises 
slightly  when  heated,  whereas  that  of  carbon  falls,  is  in 
favour  of  metallic  filament  lamps,  as  their  light  varies  less 
if  the  voltage  of  the  mains  should  be  unsteady. 

484.  Nitrogen-filled  Lamps.  —  Recently  it  has  been  found 
that  if  the  bulb  is  filled  with  very  pure  nitrogen  gas  at  about 
atmospheric  pressure,  tungsten  lamps  may  be  run  at  still 
higher  temperatures,  so  that  the  efficiency  of  a  nitrogen- 
filled  lamp  goes  up  to  2  candles  per  watt.     These  are  known 
commercially  as  "  half-watt  "  lamps,  meaning  half  a  watt 
per  candle-power.     In  many  instances  large  nitrogen-filled 
lamps  of  1000  candle-power,  consuming  about  500  watts, 
are  being  substituted  for  arc  lamps. 

485.  Nernst  Lamps.  —  Reference  was  made  in  Art.  179 
to  the  conductivity  of  hot  solid  electrolytes.     In  Nernst 's 
lamp  (1897)  a  thin  rod  of  mixed  metallic  oxides,  thoria  and 
zirconia  with  a  small  proportion  of  ceria,  looking  like  a  short 
thread  of  pipeclay,  constitutes  the  light-giving  body.     But 
to  make  it  conduct  it  must  first  be  heated  to  dull  redness 
by  an  auxiliary  electric  heater  —  a  small  wire  coil  of  high 
resistance  placed  beside  it.     So  soon  as  it  is  heated  thus,  it 
suddently  becomes  conductive  and  glows  with  great  brilliancy, 
the  light  which  it  emits  depending  on  the  peculiar  selective 
radiating  power  of  the  ceria  it  contains.     The  glower  need 
not  be  protected  from  air :  but  in  order  to  limit  the  current 
through  it,  there  is  placed  in  series  with  each  lamp  a  ballast- 


CH.  vizi.  486]  THE    ELECTRIC   ARC  463 

ing  resistance  made  of  iron  wire  enclosed  in  a  vacuous  bulb. 
The  ballasting  resistance  increases  its  resistance  with  in- 
crease of  temperature,  and  thus  when  placed  in  series  with 
the  glower  compensates  for  the  decreased  resistance  of  the 
latter  when  hot,  and  a  steady  current  is  therefore  maintained. 
Though  the  efficiency  of  this  lamp  may  be  as  high  as  04 
candle  per  watt,  the  complications  of  automatic  devices  to 
switch  the  current  from  the  heater  to  the  glower  have 
militated  against  its  use. 

LESSON  XXXIX.  —  Arc  Lamps 

486.  The  Electric  Arc.  —  If  two  pointed  pieces  of  carbon 
are  joined  by  wires  to  the  terminals  of  a  powerful  voltaic 
battery  or  other  generator  of  electric  currents,  and  are 
brought  into  contact  for  a  moment  and  then  drawn  apart 
to  a  short  distance,  a  kind  of  electric  flame  called  the  arc, 
or  "  voltaic  "  arc,  is  produced  between  the  points  of  carbon, 
and  a  brilliant  light  is  emitted  by  the  white-hot  points  of 
the  carbon  electrodes.  This  phenomenon  was  first  noticed 
by  Humphry  Davj^  in  1800,  and  its  explanation  appears  to 
be  the  following :  —  Before  contact  the  difference  of  poten- 
tial between  the  points  is  insufficient  to  permit  a  spark  to 
leap  across  even  -5-^^-5-  of  an  inch  of  air-space,  but  when 
the  carbons  are  made  to  touch,  a  current  is  established.  On 
separating  the  points  the  spark  at  parting  volatilizes  a  small 
quantity  of  carbon  between  the  points,  and  ionizes  the 
vapour  by  emission  of  electrons  from  the  hot  point  of  the 
kathode  (Art.  632),  or  negative  carbon.  Carbon  vapour 
being  a  partial  conductor  allows  the  current  to  continue  to 
flow  across  the  gap,  provided  it  be  not  too  wide ;  but  as  the 
carbon  vapour  has  a  very  high  resistance  it  becomes  in- 
tensely heated  by  the  passage  of  the  current,  and  the  carbon 
tips,  particularly  the  tip  of  the  positive  carbon,  also  grow 
hot.  Since,  however,  solid  matter  is  a  better  radiator  than 
gaseous  matter,  the  carbons,  though  they  are  not  so  hot, 


464  ELECTRICITY   AND   MAGNETISM     [PT.  n.  486 

emit  far  more  light  than  the  arc  itself,  which  is  of  a  pale 
violet  tint.  The  temperature  of  the  arc  is  simply  deter- 
mined by  the  temperature  at  which  carbon  volatilizes  ; 
about  3500°  C.  according  to  Violle.  In  the  arc  the  most 
infusible  substances,  such  as  flint  and  diamond,  melt  ;  and 
metals  such  as  gold  and  platinum  are  even  vaporized  readily 
in  its  intense  heat.  When  the  arc  is  produced  in  the  air  the 
carbons  slowly  burn  away  by  oxidization.  It  is  observed, 
also,  that  particles  of  carbon  are  volatilized  off  and  torn 
away  from  the  positive  electrode,  which  becomes  hollowed 

out  to  a  cup-shape,  or  crater,  and 
if  the  gap  between  the  carbons  is 
small  some  of  these  particles  are 
deposited  on  the  negative  elec- 
trode, which  assumes  a  pointed 
form,  as  shown  in  Fig.  275.  The 
resistance  of  the  arc  varies  with 
the  length  and  section  of  the  flame. 
The  arc  also  apparently  exerts  an 
opposing  electromotive-force  of  its 
own,  amounting  to  about  39  volts 

FIG.  275.  -  The  Electric  Arc.          when   the   ^  ^    ^^        The   ^^ 

of  this  apparent  back  electromotive-force  is  at  the  surface  of 
the  crater  where  the  work  of  volatilizing  the  carbon  is  being 
done.  If  air  gets  to  the  white-hot  crater  the  arc  becomes 
unstable  and  hisses,  and  the  back  electromotive-force  is 
much  lower.  The  voltage  V  between  the  carbons  of  a  steady 
arc  may  be  expressed  by  the  formula  :  — 


where  I  is  the  length  of  the  arc  in  mililmetres,  and  a  and  b 
are  constants  the  values  of  which  for  homogeneous  carbons 
are  respectively  about  39  and  20.  Thus  a  4-millimetre  arc 
length  takes  about  47  volts  if  the  current  is  10  amperes,  or 
55  volts  if  the  current  is  5  amperes.  It  is  necessary  also 


CH.  vm.  486]  THE   ELECTRIC   ARC  465 

that  there  should  be  in  series  with  the  arc  a  "  ballasting  " 
resistance  of  about  1  ohm  or  more  to  steady  the  current. 
Without  this  the  arc  would  practically  be  a  short-circuit. 

To  produce  an  electric  arc  satisfactorily  a  minimum 
electromotive-force  of  45  to  60  volts  is  necessary  if  continu- 
ous currents  are  used.  With  alternating  currents  30  to  35 
volts  suffice.  The  usual  current  for  arc  lamps  of  400  to  800 
candle-power  is  from  5  to  10  amperes.  With  weaker  cur- 
rents or  smaller  electromotive-forces  it  is  difficult  to  maintain 
a  steady  arc.  For  an  ordinary  arc  the  efficiency  is  about  1-5 
candles  per  watt.  The  common  size  of  carbon  rod  in  use  is 
10  or  11  millimetres  in  diameter  :  the  consumption  is  roughly 
1  inch  per  hour ;  the  +  carbon  consuming  much  faster  than 
the  —  carbon.  Being  a  flexible  conductor,  the  arc  can  be 
deflected  by  a  magnet.  The  arc  is  sensitive  to  draughts 
and  must  be  protected  by  a  globe.  For  search-lights  on 
board  ship  and  for  lighthouses,  arc  lights  of  greater  power 
are  produced  by  using  thicker  carbons  and  supplying  them 
with  currents  of  20  to  100  amperes  or  more.  Enclosed  arcs 
from  which  free  access  of  air  is  excluded,  consume  their 
carbons  about  twenty  times  slower ;  they  work  with  longer 
arcs  and  require  about  75  to  85  volts.  Their  efficiency  is 
about  0-9  candle  per  watt.  In  practical  electric  lighting, 
the  generator  is  always  a  dynamo-electric  machine  (Arts. 
506  to  514).  The  internal  resistance  of  ordinary  DanielPs 
or  Leclanche's  cells  is  too  great  to  render  them  serviceable 
for  producing  arc  lights.  Moreover,  a  battery  of  40  to  60 
Grove's  cells  (Art.  190)  will  not  continue  the  supply  more 
than  2  or  3  hours.  The  quantity  of  light  emitted  by  an  arc 
lamp  differs  in  different  directions,  the  greatest  amount 
being  emitted  (when  the  -f  carbon  is  at  the  top)  at  an  angle 
of  about  45°  downwards.  The  bottom  carbon  and  its 
holder  cut  off  much  light  in  the  direction  vertically  down- 
wards. Fig.  276  gives  a  graphic  curve  of  the  distribution, 
the  radial  lines  showing  by  their  relative  lengths  the  amounts 
of  light  emitted.  About  85  per  cent  of  the  light  comes 
2H 


466 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  487 


90      60       70        60 


FIG.  276. 


from  the  white-hot  crater,  very  little  from  the  negative  tip. 
Inverted  arcs  are  those  with  the  +  carbon  at  the  bottom  in 
order  to  throw  the  light  upwards  to  the  ceiling.  The  name 
of  flame  arcs  is  given  to  those  in  which  certain  chemicals 
such  as  calcium  fluoride  or  aluminium  fluoride  are  added  to 
the  carbon  in  order  to  colour  the  flame.  In  these  much  of 
the  light  is  emitted  by  the  flame  itself.  Their  efficiency  is 

about  4  candles  per  watt. 
In  the  alternating-current 
arc  the  carbon  points  are 
alike  and  emit  equal  light. 
The  frequency  of  alterna- 
tion should  be  at  least  40 
periods  per  second.  The 
total  quantity  of  light 
Distribution  of  Light  of  the  Arc.  emitted,  when  the  current 

is  supplied  at  a  fixed  voltage,  is  not  quite  proportional 
to  the  current,  but  increases  in  a  somewhat  higher  ratio. 
Doubling  the  current  makes  rather  more  than  twice  as  much 
light :  it  doubles  the  size  of  the  luminous  crater.  Each 
square  millimetre  of  the  crater  surface  emits  normally  a  light 
of  about  170  candles. 

487.  Arc  Lamps.  —  Davy  employed  wood  charcoal  for 
electrodes  to  obtain  the  arc  light.  Pencils  of  hard  gas- 
carbon  were  later  introduced  by  Foucault.  In  all  the  more 
recent  arc  lamps,  pencils  of  a  more  dense  and  homogeneous 
artificial  coke-carbon  are  used.  These  consume  away  more 
regularly,  and  less  rapidly,  but  some  automatic  contrivance 
is  necessary  to  push  the  points  of  the  carbons  forward  as 
fast  as  needed.  The  mechanism  of  the  arc  lamp  should 
"  strike  "  the  arc  by  causing  the  pencils  to  touch,  and  then 
separate  them  to  the  requisite  distance,  about  5  millimetres  ; 
the  mechanism  should  also  "  feed  "  the  carbons  into  the 
arc  as  fast  as  they  are  consumed ;  and  it  should  also  cause 
the  points  to  approach  or  recede  automatically  in  case  the 
arc  becomes  too  long  or  too  short;  it  should  further  bring 


CH.  viii.  488,  489] 


ARC   LAMPS 


467 


the  carbons  together  for  an  instant  to  strike  the  arc  again, 
if  by  any  chance  the  flame  goes  out.  Arc  Lamps,  fulfilling 
these  conditions,  have  been  invented  by  a  number  of  persons. 
The  earliest  was  invented  in  1847  by  W.  E.  Staite.  If  the 
condition  of  supply  is  constant  voltage  the  arc  lamps  must 
be  connected  in  parallel;  if  arc  lamps  are  to  be  run  in  series, 
the  same  current  flowing  in  succession  through  each  of  the 
lamps,  then  the  supply  must  be  of  a  current  of  unvarying 
strength.  In  this  case  a  shunt  circuit  in  each  lamp  to  work 
the  mechanism  is  necessary. 

488.  Classification  of  Arc  Lamps.  —  Arc  lamps  may  also 
be  classified  according  to  the  electrical  arrangements  that  con- 
trol the  mechanism,  there  being  three  types  according  to 
whether  the  electromagnet  is  of 

thick  wire  in  the  main  circuit  in 
series  with  the  arc,  or  is  of  fine 
wire  and  in  shunt  with  the  arc; 
or,  in  the  third  case,  both  sorts 
are  present.  The  table  on  follow- 
ing page  sets  forth  these  different 
varieties. 

489.  Mechanism  of  Arc  Lamps. 
—  Arc   lamps   may   be  classified 

in  respect  of  their  mechanism  as 
follows : 

(a)  Clockwork  Lamps.  —  In  an 
early  pattern  of  "  regulator  "  de- 
signed by  Foucault  the  carbon- 
holders  were  propelled  by  a  train 

Of      Clockwork      Wheels       actuated     FIG.  277.  —  Mechanism  of  a  Shunt 

by  a  spring.     An  electromagnet  Lamp> 

through  which  the  current  runs,  attracts  an  armature  and 
governs  the  clockwork,  causing  the  carbons  to  part  from  or 
approach  to  one  another  as  required.  In  many  modern  arc 
lamps  the  weight  of  the  carbon-holders  drives  the  clockwork 
mechanism.  Of  this  class  was  Serrin's  lamp,  which  from 


468 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  489 


If 

02  **~* 

a?   b£ 

N 

6..-S 

II 


II 

&>  O 


g. 


II 


11 

6° 


73 
,-  S 
I  ^ 
5  ° 

Oj     02 

a§ 
It 

•so 


I 
1 


If 


ft  c^o 

w    OiO 


3 


«I1§ 

»    H    H    S 

f^CC    ft  ^ 


CH.  viii.  489]          ARC   LAMP  MECHANISM 


469 


1855  onwards  was  largely  used  for  lighthouses.  A  modern 
sort  of  clockwork  lamp  is  depicted  diagrammatically  in 
Fig.  277.  Here  a  flexible  band  which  connects  the  carbon- 
holders  passes  round  a  pulley  and  drives  a  train  of  geared 
wheels.  The  train  is  mounted  to  rock  about  a  pivot  at  C. 
If  the  train  is  rocked  over  to  the  left  the  last  wheel  of  the 
train  is  locked  against  a  detent  D,  and  at  the  same  time  the 
pulley  is  raised  a  little,  thus  lifting  the  top  carbon.  If  the 
train  is  rocked  over  to  the  right  the  wheel  work  is  released, 
and  lets  the  top  carbon  run  down.  In 
the  arrangement  shown,  an  electro- 
magnet M  (connected  in  shunt)  pulls 
the  train  over  to  the  right,  and  is 
opposed  by  a  spring  S  which  pulls  the 
train  to  the  left  when  there  is  no  cur- 
rent on.  Hence  when  not  in  use  the 
carbons  are  apart.  So  soon  as  the  cur- 
rent is  switched  on,  the  shunt  electro- 
magnet pulls  strongly,  and  the  top 
carbon  runs  down  into  contact.  When 
the  carbons  touch,  the  current  in  the 
shunt  circuit  weakens,  and  the  spring  S 
pulls  the  rocking  frame  over  and  parts 
the  carbons,  thus  striking  the  arc. 
When  the  arc  grows  long,  more  current 
flows  round  the  shunt,  which  will  then 
rock  the  frame  over  to  the  right, 
finally  causing  feeding  to  occur. 

(6)  Brake-wheel  Lamps.  —  Another  mechanism  for  regu- 
lating the  rate  of  feeding  the  carbon  into  the  arc  consists 
in  the  application  of  a  brake-wheel ;  the  brake  which  stops 
the  wheel  being  actuated  by  an  electromagnet  which 
momentarily  releases  the  brake  and  allows  the  wheel  to  run 
forward  a  little  when  the  resistance  of  the  arc  increases 
beyond  its  normal  amount.  In  Fig.  278  B  is  the  brake- 
wheel,  L  the  lever  which  governs  it,  C  an  iron  core  of  the 


FIG.  278.  —  Mechanism  of  a 
Brake-wheel  Lamp. 


470  ELECTRICITY   AND   MAGNETISM     [PT.  n.  490 

coil  S  inserted  in  series  in  the  circuit.  When  current  is 
switched  on,  the  core  is  drawn  up,  causing  L  to  grip  B  and 
to  turn  it  a  little,  so  parting  the  carbons  and  striking  the  arc. 

(c)  Solenoid  Lamps.  —  In  this  class  of  arc  lamp  the  move- 
ment of  one  or  both  of  the  carbons  is  governed  by  an  iron 
plunger  capable  of  sliding  vertically  up  or  down  inside  a 
hollow  coil  or  solenoid,  which,  being  traversed  by  the  cur- 
rent, thus  regulates  the  length  of  the  arc.     Siemens  employed 
two  solenoids  acting  against  one  another  differentially,  one 
being  a  main-circuit  coil,  the  other  being  a  fine-wire  coil 
connected  as  a  shunt  to  the  arc.     The  shunt  coil  acts  as  a 
voltmeter  to  watch  the  arc  and  feed  the  carbons  forward  when 
the  volts  rise  above  the  normal  ;   it  being  set  to  control  the 
feeding  mechanism. 

(d)  Clutch  Lamps.  —  A  somewhat  simpler  device  is  that 
of  employing  a  clutch  to  pick  up  the  upper  carbon-holder, 
the  lower  carbon  remaining  fixed.     In  this  kind  of  lamp  the 
clutch  is  worked  by  an  electromagnet,  through  which  the 
main  current  passes.     If  the  lamp  goes  out  the  magnet  re- 
leases the  clutch,  and  the  upper  carbon  falls  by  its  own 
weight  and  touches  the  lower  carbon.     Instantly  the  current 
flows  round  the  electromagnet,  which  causes  the  clutch  to 
grip  the  carbon-holder,  and  raise  it  to  the  requisite  distance. 
Should  the  arc  grow  too  long,  the  lessening  attraction  on  the 

clutch  automatically  permits  the  car- 
bon-holder to  advance  a  little. 

(e)  Motor  Lamps.  —  Sometimes  little 
electric  motors  are  used  to  operate  the 
carbons  automatically. 

490.    Projector  Lamps.  —  For  opti- 
cal   lanterns    and    for    search-lights, 
special   forms   of   arc   lamp   are  con- 
FIG.  279.  —  Hand-feed  Pro-    structed    to    throw    a    concentrated 

jectorLamp. 


are    usually    either    tilted    back    as    in    Fig.    279,    or    set 
at  right  angles  to  one  another  as  in  Fig.  280,  so  that  the 


CH.  viii.  491-493]      ELECTRIC    CANDLES 


471 


crater  throws  most  of  its  light  for- 
ward. The  concentration  of  the 
beam  is  effected  by  condenser  lenses, 
or  by  parabolic  mirrors. 

491.  Flame  Arc  Lamps.  —  Flame  arc 
lamps  are  generally  designed  with  the    FIG.  230.  —  Arrangement  of 

Carbon-holders      Sloping      downwards       Carbons  in  a  Projector  Lamp. 

like  the  letter  V,  and  so  arranged  that  one  or  both  of  them 
swing  so  that  the  tips  can  be  brought  together  and  moved 
apart.  The  flame  is  therefore  at  the 
,  J|}__  lowest  point,  and  casts  the  light  chiefly 

downwards.  Fig.  281  shows  a  design 
in  which  the  two  carbons,  sliding  in 
guides,  are  propelled  by  a  counter- 
poise weight.  Automatic  mechanism 
similar  to  that  already  described  is 
necessary  to  govern  the  movement; 
striking  the  arc  by  momentarily  caus- 
ing the  carbons  to  touch,  and  feeding 
the  carbons  downward  as 
they  are  consumed. 

492.  Electric  Candles.  - 
To  obviate  the  expense  and 
complication  of  mechanism, 
electric  candles  have  been 
suggested.  Fig.  282  depicts 
Jablochkoff's  candle,  consist- 
ing of  two  parallel  pencils  of 
hard  carbon  separated  by  a 
thin  layer  of  plaster  of  Paris 

and  supported  in  an  upright  holder.      The  arc 
plays  across  the  summit  between  the  two  carbon  FlG   282 
wicks.     In  order  that  both  carbons  may  consume 
at  equal  rates,  alternating  currents  were  employed. 

493.    The   Magnetite  Arc.  —  In  this  American  lamp  the 
positive  electrode  consists  of  a  copper  piece  which  does  not 


FIG.  281.  —  Flame  Arc 
Lamp. 


Candle. 


472          ELECTRICITY  AND   MAGNETISM    [PT.  n.  494,  495 

consume,  while  the  bottom  or  negative  electrode  is  a  cart- 
ridge about  eight  inches  long  packed  with  a  mixture  of  black 
oxide  of  iron  (magnetite)  with  titanium  oxide.  The  light, 
which  in  this  lamp  comes  solely  from  the  flame,  is  thrown 
out  sideways.  The  arc  is  about  half  an  inch  long.  On  a 
100- volt  continuous  current  circuit  it  takes  about  4  amperes  ; 
and  as  the  intensity  is  about  1000  candles,  the  efficiency  is 
high,  being  about  2-5  candles  per  watt.  But  the  illumina- 
tion is  not  always  steady. 

494.  Action  of   Magnets  on  the  Arc.  —  An  arc  being  a 
flexible  conductor  is  capable  of  being  dragged  laterally  by  a 
magnetic  field.     The  force  acting  on  the  arc  is  at  right 
angles  to  the  current  and  to  the  lines  of  the  magnetic  field. 
If  a  north  magnetic  pole  is  presented  towards  a  vertical  arc 
with  the  current  flowing  downwards,  the  arc  bends  outward 
towards  the  right.     If  a  south  pole  is  presented,  the  down- 
ward flowing  arc  is  bent  towards  the  left.     It  may  even  be 
blown  out  and  extinguished  if  the  magnet  is  strong.     An 
arc  may  be  caused  to  rotate  round  a  magnetic  pole  if  a  tubu- 
lar carbon  is  used  with  the  magnet  inside  it.     If  the  poles 
of  a  horseshoe  magnet  or  electromagnet  are  placed  at  the 
sides  of  an  arc,  so  that  the  current  crosses  the  field  between 
the  poles,  the  arc  is  blown  out  into  a  pointed  form  resembling 
a  blow-pipe  flame.     A  process  called  arc  welding  is  used,  in 
which  such  an  electric  blow-pipe  is  employed.     An  arrange- 
ment called  a  magnetic  blow-out  is  used  for  extinguishing  an 
arc  that  may  be  casually  formed  between  the  contacts  of  a 
circuit-breaker  or  of  a  controller. 

495.  The  Singing  Arc.  —  It  was  independently  found  by 
Elihu  Thomson  and  by  Duddell  that  if  a  continuous  current 
arc  is  shunted  by  a  circuit  containing  a  self-induction  coil 
or  a  self-induction  coil  in  series  with  a  condenser,  the  arc  is 
thrown  into  rapid  oscillations  and  emits  a  musical  sound, 
the  pitch  of  which  depends  on  the  inductance  and  capacity 
of  the  circuit.     Poulsen  has  made  this  discovery  the  basis  of 
his  method  of  radio-telegraphy  (Art.  624).     The  effect  is 


CH.  vm.  496]  VAPOUR    LAMPS  473 

enhanced  if  the  arc  is  enclosed  in  coal-gas  or  a  hydrocarbon 
vapour. 

496.  Vapour  Lamps.  —  There  are  several  forms  of  vapour 
lamps  in  which  the  light  is  emitted  entirely  from  luminous 
conducting  vapours  or  gases.  The  vapour  of  mercury  en- 
closed in  a  vacuum  tube  (Art.  342)  gives  out  an  intense  green 
light  when  a  current  is  passed  through  it,  and  is  utilized  in 
the  Cooper-Hewitt  lamp.  The  light  is,  however,  a  combina- 
tion of  violet,  blue,  green,  and  yellow,  the  red  rays  being 
entirely  absent,  and  therefore  the  light  is  not  white.  The 
light  of  this  lamp  being  rich  in  ultra-violet  rays  is  strongly 
actinic,  and  is  very  suitable  for  indoor  photographic  studios. 
The  efficiency  of  this  type  of  lamp  is  about  2  candles  per  watt. 

Another  vapour  lamp  is  the  Moore  tube  light,  which  con- 
sists of  a  long  tube  containing  carbon  dioxide  or  nitrogen  at 
low  pressure,  and  is  supplied  with  a  high-tension  alternating 
current.  The  pressure  of  the  gas  is  kept  constant  within 
the  tube  by  an  electromagnetically  operated  valve.  The 
light  given  out  by  the  tube  when  filled  with  carbon  dioxide 
is  nearly  white.  The  efficiency  of  the  lamp  is  about  0-5 
candle  per  watt.  A  tube  similar  to  the  above,  but  filled 
with  the  rare  gas  neon,  has  an  efficiency  of  2  candles  per 
watt. 


CHAPTER  IX 

INDUCTANCE 

LESSON  XL.  —  Mutual  Inductance 

497.  Mutual  Inductance.  —  The  operation  of  mutual  in- 
duction between  two  circuits,  a  primary  and  a  secondary, 
was  briefly  considered  in  Art.  241.  Let  us  now  consider 
the  electromotive-forces  so  induced.  Suppose  the  primary 
coil  to  have  Si  spirals,  and  the  secondary  coil  S2  spirals. 
At  first  let  them  be  arranged  (by  use  of  an  iron  core  or  by 
geometric  juxtaposition)  so  that  all  the  magnetic  lines  evoked 
by  the  primary  coil  pass  through  all  the  spirals  of  the  second- 
ary coil  ;  both  coils  being  placed  close  together  upon  a  suit- 
able core  of  laminated  iron. 

By  Art.  405  the  magnetic  flux  g  due  to  current  i  in  the 
primary  coil  will  be 

3  =  iSi/Z, 

where  Z  is  the  reluctance  (Art.  404)  of  the  magnetic  circuit, 

and  is  equal  to  —  —  X  —  if  the  core  has  length  I,  sectional  area 
Ayu,      4^r 

A,  and  permeability  u.  The  total  amount  of  cutting  mag- 
netic lines  by  the  S2  spirals  of  the  secondary,  when  current 
i  is  turned  off  or  on,  will  be 


Hence  it  follows  that  the  amount  of  cutting  of  magnetic 
lines  (i.e.  the  induction  in  the  secondary  circuit)  due  to  turn- 
ing on  or  off  1  ampere  in  the  primary,  will  be  SiS2/Z.  This 
quantity  is  denoted  for  brevity  by  the  symbol  M.  If  the 
primary  and  secondary  coils  are  not  so  arranged  that  all  the 

474 


CH.  ix.  498]  INDUCED   CURRENTS  475 

magnetic  lines  due  to  the  one  pass  through  the  spirals  of  the 
other,  then  M  will  have  a  less  value  than  SiS2/Z. 

The  practical  unit  for  coefficients  of  mutual  inductance 
is  the  same  as  for  those  of  self-inductance,  namely  the  henry 
(Arts.  381  and  501),  and  is  109  C.G.S.  units.  So,  as  the 
ampere  is  10"1  of  the  absolute  unit  of  current,  in  order  to 
bring  M  to  henries  we  must  divide  the  above  value  by  108. 

If  the  current  in  the  primary  is  varying  at  the  rate  di/dt, 
the  electromotive-force  E2  thereby  induced  in  the  secondary 
circuit  will  be 

E2  =  -  M  •  di/dt, 

where  E2  will  be  in  volts  if  M  is  expressed  in  henries,  i  in 
amperes,  and  t  in  seconds. 

The  value  of  M  for  the  small  induction  coils  used  in  tele- 
phone work  is  usually  about  0-01  henry ;  for  a  Ruhmkorff 
coil  capable  of  giving  a  spark  10  centimetres  long  it  may  be 
as  much  as  from  5  to  20  henries. 

Example.  —  Suppose  in  a  spark-coil  the  value  of  M  is  8  henries, 
and  the  primary  current  changes  by  an  amount  of  1 
ampere  in  one  ten- thousandth  of  a  second  (owing  to  the 
quick-acting  break),  the  electromotive-force  induced  in 
the  secondary  during  that  ten-thousandth  of  a  second  will 
be  80,000  volts. 

To  measure  a  coefficient  of  mutual  inductance,  there  are 
several  methods,  some  of  which  depend  on  the  use  of  Wheat- 
stone's  bridge;  but  the  best  method  is  one  due  to  Carey 
Foster.  In  this  the  quantity  of  electricity  discharged  from 
a  condenser  of  known  capacity  C,  shunted  by  a  resistance  p 
in  the  primary  circuit,  is  balanced  against  the  quantity  dis- 
charged in  the  secondary  circuit  by  regulating  a  resistance 
q  in  the  latter.  Then  M  =  Cpq. 

498.  Induced  Currents  of  Higher  Orders.  —  Joseph 
Henry,  an  independent  discoverer  of  magneto-electric  induc- 
tion, observed  that  the  variations  in  the  strength  of  the 
secondary  current  could  induce  tertiary  currents  in  a  third 
closed  circuit,  and  that  variations  in  the  tertiary  currents 


476        ELECTRICITY  AND   MAGNETISM     [PT.  n.  499,  500 

might  induce  currents  of  a  fourth  order,  and  so  on.  A  single 
sudden  primary  current  produces  two  secondary  currents 
(one  inverse  and  one  direct),  each  of  these  produces  two 
tertiary  currents,  or  four  tertiary  currents  in  all.  But  with 
alternating  currents  there  are  the  same  number  of  secondary 
and  tertiary  fluctuations  as  of  primary ;  but  the  currents  of 
the  second,  fourth,  etc.  orders  will  be  inverse,  in  the  direction 
of  their  flow,  to  those  of  the  first,  third,  fifth,  etc. 

499.  Lenz's  Law.  —  In  Art.  240  it  was  explained  how  an 
increase  in  the  number  of  magnetic  lines  through  a  circuit 
(as  by  pushing  in  a  magnet)  tended  to  set  up  an  inverse 
current,  or  one  flowing  in  such  a  direction  as  is  opposed  to 
the  magnetism,  and  therefore  tends  to  push  the  magnet  back. 
Similarly  a  decrease  in  the  magnetic  lines  (as  by  withdrawing 
the  magnet)  tends  to  set  up  currents  that  will  pull  the  mag- 
net back  again.     Lenz  x  summed  up  the  matter  by  saying 
that  in  all  cases  of  electromagnetic  induction  caused  by  mechani- 
cal movement,  the  induced  currents  have  such  a  direction  that 
their  reaction  tends  to  stop  the  motion  which  produces  them. 
This  is  known  as  Lenz's  law :   it  is  a  particular  case  of  the 
more  general  law  of  reaction  applicable  to  all  electromagnetic 
systems,  namely,  that  every  action  on  such  a  system,  which, 
in  producing  a  change  in  its  configuration  or  state,  involves  a 
transformation  of  energy,  sets  up  reactions  tending  to  preserve 
unchanged  the  configuration  or  state  of  that  system.     (Compare 
Arts.  217  and  409.) 

500.  Eddy-Currents  Induced  in  Masses  of  Metal.  —  In 
1824  Gambey  found  that  a  compass-needle  oscillating  in  its 
box  came  to  rest  sooner  if  the  bottom  of  the  box  were  made 
of  metal  than  if  of  wood.     Arago  investigated  the  matter, 
and  found  a  copper  plate  under  the  needle  most  effective  in 
damping  its  motions.     He  then  rotated  a  copper  disk  in  its 
own  plane  underneath  a  compass-needle,  and  found  that  the 
needle  was  dragged  round  as  by  some  invisible  friction.     A 
copper  disk  suspended  over  a  rotating  magnet  was  found  to 

1  Lenz,  Poggendorffs  Annalen,  xxi,  p.  484,  1834. 


CH.  ix.  500]  EDDY-CURRENTS  477 

be  dragged  by  it.  Attempts  were  made  to  account  for  these 
phenomena  —  known  as  Arago's  rotations  —  by  supposing 
there  to  be  a  sort  of  magnetism  of  rotation,  until  Faraday 
proved  them  to  be  due  to  induction.  A  magnet  moved  near 
a  solid  mass  or  plate  of  metal  induces  in  it  currents  which, 
in  flowing  through  it  from  one  point  to  another,  have  their 
energy  eventually  frittered  down  into  heat,  and  which,  while 
they  last,  produce  (in  accordance  with  Lenz's  law)  electro- 
magnetic forces  tending  to  stop  the  motion.  These  currents, 
circulating  wholly  within  the  metal,  and  not  confined  to 
particular  paths  along  insulated  wires,  are  called  eddy- 
currents.  If  a  cube  or  ball  of  good  conducting  metal  be  set 
spinning  between  the  poles  of  such  an  electromagnet  as  Fig. 
207,  and  the  current  be  suddenly  turned  on,  the  spinning 
metal  stops  suddenly.  In  a  copper 
disk  revolving  between  the  poles  of  a 
magnet  (Fig.  283)  there  are  a  pair  of 
eddies  in  the  part  passing  between  the 
poles,  and  these  currents  tend  to  pull 
the  disk  back.  In  fact,  any  conductor 
moved  forcibly  across  the  lines  of  a  FIG.  283.  —  Eddy-currents  in 

.  a  Rotating  Disk. 

magnetic  field  experiences  a  mechanical 

resistance  due  to  the  induced  currents  which  oppose  its 
motion.  Joule  in  1843,  and  Foucault  in  1855,  showed  1  that 
if,  by  sheer  force,  a  disk  or  mass  of  metal  be  kept  spinning 
between  the  poles  of  a  powerful  magnet  it  will  become  hot 
in  consequence  of  the  eddy-currents  induced  in  it. 

The  eddy-current  drag  on  a  moving  conductor  (sometimes 
called  the  magnetic  friction)  is  a  force  proportional  to  the 
speed  and  proportional  to  the  square  of  the  magnetic  field ; 
for  the  force  (Art.  367)  is  proportional  to  the  product  of 
field  and  current,  and  the  current  (circulating  round  a  given 
path)  is  proportional  both  to  field  and  to  speed.  Hence 
eddy-current  drag  is  employed  in  some  forms  of  electric 

1  Hence  some  writers  call  the  eddy-currents  "Foucault's  currents," 
though  they  were  known  years  before  Foucault's  experiments  were  made. 


478  ELECTRICITY   AND   MAGNETISM     [PT.  n.  501 

supply  meter  (Art.  460)  as  a  brake  to  control  the  speed  of 
the  moving  part.  Since  the  drag  is  proportional  to  the  speed 
when  the  field  is  constant,  a  speed-counter  may  be  made  on 
this  principle,  by  revolving  a  permanent  magnet  so  that  it 
drags  upon  a  thin  aluminium  disk  or  cup  that  is  mounted  on 
a  pivot  and  controlled  by  a  spring.  An  index  attached  to 
the  pivoted  disk  indicates  on  a  scale  the  number  of  revolu- 
tions per  minute  of  the  magnet. 

Alternating  electric  currents  also  set  up  parasitic  eddy- 
currents  in  masses  of  metal  near  them ;  for  this  reason  the 
iron  cores  of  transformers  (Art.  538)  and  of  dynamo  arma- 
tures (Art.  508)  must  be  carefully  laminated,  otherwise  there 
will  be  heating  and  waste  of  energy.  The  high  resistance 
of  stalloy  (Art.  391)  is  here  advantageous.  Further,  eddy- 
currents  in  any  mass  of  metal  between  a  primary  and  a 
secondary  circuit  will  tend  to  set  up,  in  the  secondary  cir- 
cuit, electromotive-forces  opposing  those  set  up  by  the 
primary.  Hence  interposed  sheets  of  metal  act  as  induction- 
screens. 

LESSON  XLI.  —  Self -Inductance 

501.  Self-Inductance.  —  It  has  been  pointed  out  in  Art. 
241  how  when  a  current  in  a  circuit  is  increasing  or  diminish- 
ing, it  exercises  an  inductive  effect  upon  any  neighbouring 
circuit ;  this  inductive  effect  being  due  to  the  change  in  the 
magnetic  field  surrounding  the  varying  current.  But  since 
the  magnetic  lines  surrounding  a  current  may,  as  they  move 
inwards  or  outwards  from  the  wire,  cut  across  other  parts  of 
the  same  circuit,  it  is  evident  that  a  current  may  act  in- 
ductively on  itself.  The  self-inductive  action  is  great  if  the 
circuit  consists  of  a  coil  of  many  turns,  and  is  still  greater  if 
the  coil  possesses  an  iron  core.  Suppose  a  coil  of  wire  to 
possess  S  spirals,  and  that  it  generates  a  magnetic  flux 
through  these  spirals  of  g  lines  when  current  i  is  turned  on. 
Then  it  is  clear  that  turning  on  the  current  will  have  the 
same  effect  as  if  a  magnet  of  g  lines  were  suddenly  plunged 


CH.  ix.  501]  SELF-INDUCTANCE  479 

into  the  coil ;  and  turning  off  the  current  will  have  the  same 
effect  as  if  the  magnet  were  suddenly  withdrawn.  Now 
(Art.  243)  the  current  induced  by  plunging  a  magnet  into  a 
coil  is  an  inverse  current  tending  to  push  it  out,  while  that 
induced  by  withdrawing  the  magnet  is  a  direct  current,  tend- 
ing to  attract  it  back.  It  follows  that  the  self-induced 
electromotive-force  on  turning  the  current  on,  will  tend  to 
oppose  the  current,  and  prevent  it  growing  as  quickly  as  it 
otherwise  would  do;  while  that  induced  on  stopping  the' 
current  will  tend  to  help  the  current  to  continue  flowing. 
In  both  these  cases  the  effect  of  self-induction  is  to  oppose 
change :  it  acts  as  an  electro-magnetic  inertia. 

In  the  case  supposed  above,  where  the  coil  has  S  turns, 
the  total  cutting  of  magnetic  lines  in  the  operation  will 
=  S  X  8,  provided  all  the  lines  thread  through  all  the 
spirals.  Let  the  symbol  L  be  used  to  represent  the  total 
amount  of  cutting  of  lines  by  the  circuit  when  a  current 
of  1  ampere  is  suddenly  turned  on  or  off  in  it.  Clearly 
L  X  i  =  S  X  g.  This  quantity  L  is  called  "  the  induct- 
ance "  of  the  circuit.  It  was  formerly  called  "  the  coefficient 
of  self-induction  "  of  the  circuit.  The  unit  of  inductance  is 
named  the  henry,  and  corresponds  to  a  cutting  of  108  mag- 
netic lines  when  1  ampere  is  turned  on  or  off.  Since  (in 
circuits  without  iron  cores)  g  is  proportional  to  S,  it  follows 
that  L  is  proportional  to  S2.  For  since  (see  Art.  405) 
g  =  iS/Z,  the  interlinkage  of  lines  is 

s  x  g  =  Li  =  ;syz. 

Hence  when  one  ampere  is  turned  on  or  off  the  inductance 
will  be 

L  =  S2/Z, 

which  may  be  expressed  in  henries  by  dividing  by  108.  If 
all  the  lines  do  not  pass  through  all  the  spirals  the  value  of 
L  will  be  less  than  this. 

The  self-induced  electromotive-force  will  depend  upon  the 


480  ELECTRICITY   AND   MAGNETISM     [PT.  n.  502 

rate  at  which  the  current  is  changing  ;  for  if  the  total  cutting 
Sg  take  place  in  time  t,  it  follows  (Art.  243)  that 

E  =  -  Sg/£  =  -  Li/t. 


But  since  the  rate  at  which  the  current  changes  is  not  uni- 
form, E  is  also  not  uniform.  If  in  an  element  of  time  dt  the 
current  changes  by  an  amount  di,  the  rate  of  change  of  the 
current  is  di/dt,  and  the  self-induced  electromotive-force  is 
=  -  L  •  di/dt. 

The  formal  definition  of  the  henry  (Art.  381)  is  based  on 
this  expression  in  order  that  it  may  apply  to  circuits  with 
iron  cores  as  well  as  to  circuits  without  them. 

The  energy  of  the  magnetic  field  surrounding  the  current 
is  equal  to  \  Li2,  since,  while  the  field  is  growing  up  to  have 
Li  lines  in  total,  the  average  value  of  the  current  is  J  i. 

502.  Measurement  of  Self-Inductance.  —  To  measure  a 
coefficient  of  self  -inductance  there  are  several  methods  :  — 

(a)  Alternating-current     Method.  —  The     volts     V     re- 
quired   to    send    current   i   at    frequency   n    through    coil 
having  resistance  R  and  coefficient  of  self-inductance  L  are 
V  =  i  VR2  4-  4  7r2n2L2  ;    or,  if  the   resistance   is   negligible, 
V  =  27rmL;   whence  L  =  V/2  irni  (see  Art.  525). 

(b)  Bridge  Methods.  —  Of  several  bridge  methods  the  best 
is  Maxwell's.     Let  balance  be  obtained  in  usual  way;   key 
in  battery  circuit  being  put  down  before  key  in  galvanometer 
circuit  (Art.  446).     Then  press  the  keys  in  reverse  order, 
when  the  presence  of  self-induction  in  one  of  the  four  arms 
will  upset  balance,  the  needle  giving  a  kick  a  proportional 
to  the  self-induction.     Now  introduce  in  the  same  arm  an 
additional  small  resistance  r,  such  that  when  keys  are  again 
operated  in  the  usual  order  there  is  a  small  permanent  de- 
flexion B.     If  the  periodic  time  of  swing  of  the  needle  be  T 
the  following  formula  then  holds  :  —  L  =  Tra/2  71-8. 

(c)  Secohmmeter  Method.  —  Ayrton  and  Perry  invented  an 
instrument  which  alternately  makes  and  breaks  the  battery 
circuit  of  the  bridge  and  only  allows  the  galvanometer  to  be 


CH.  ix.  503]          EFFECTS   OF   INDUCTANCE  481 

in  operation  during  a  short  interval  of  time  T  immediately 
after  each  making  of  the  battery  circuit  (the  galvanometer  at 
other  times  being  short-circuited).  As  the  current  is  in- 
creasing during  this  interval,  the  self-induction  L  of  a  coil 
placed  in  one  of  the  arms  of  the  bridge  acts  as  though  there 
were  an  additional  resistance  r  in  that  arm.  The  formula 
is  then,  L  =  Tr.  As  L  is  then  the  product  of  seconds  and 
ohms,  Ayrton  and  Perry  proposed  for  the  unit  the  name  of 
secohm,  now  abandoned  in  favour  of  the  name  henry. 

503.  Effects  of  Inductance.  —  The  presence  of  inductance 
in  a  circuit  affects  the  currents  in  several  ways.  The  special 
choking-effect  on  alternating  currents  is  dealt  with  in  Art. 
530.  The  effects  on  battery  currents  are  also  important. 
So  long  as  the  current  is  not  changing  in  strength,  inductance 
has  no  effect  whatever ;  but  while  the  current  is  growing  or 
while  it  is  dying  away  the  presence  of  inductance  greatly 
affects  it.  In  all  cases  inductance  tends  to  oppose  any 
change  in  the  strength  of  the  current ;  as  may  be  foreseen 
from  the  general  law  of  reaction  (Art.  499).  When  a  current 
is  increasing,  inductance  causes  it  to  increase  more  slowly. 
When  a  current  is  dying  away,  inductance  tends  to  prolong  it. 

The  existence  of  inductance  in  a  circuit  is  attested  by  the 
so-called  extra-current,  which  makes  its  appearance  as  a 
bright  spark  at  the  moment  of  breaking  circuit.  If  the  cir- 
cuit be  a  simple  one,  and  consist  of  a  straight  wire  and  a 
parallel  return  wire,  there  will  be  little  or  no  inductance; 
but  if  the  circuit  be  coiled  up,  especially  if  it  be  coiled  round 
an  iron  core,  as  in  an  electromagnet,  then  on  breaking  circuit 
there  will  be  a  brilliant  spark,  and  a  person  holding  the  two 
ends  of  the  wires  between  which  the  circuit  is  broken  may 
receive  a  shock,  owing  to  the  high  electromotive-force  of  this 
self -induced  extra  current.  This  spark  represents  the  energy, 
of  the  magnetic  field  surrounding  the  wire,  suddenly  return- 
ing back  into  the  circuit.  The  extra-current  on  "  making  " 
circuit  is  an  inverse  current,  and  gives  no  spark,  but  it  pre- 
vents the  battery  current  from  rising  at  once  to  its  full  value. 
2i 


482  ELECTRICITY   AND   MAGNETISM     [PT.  n.  504 

The  extra-current  on  breaking  circuit  is  a  direct  current, 
and  therefore  tends  to  keep  up  the  strength  of  the  current 
just  at  the  moment  when  it  is  about  to  cease.  To  avoid  the 
perturbing  effects  of  inductance,  resistance-coils  are  always 
coiled  back  upon  themselves  (Art.  446) ;  i.e.  wound  non- 
inductively. 

Even  when  a  circuit  consists  of  two  parallel  straight  wires 
there  is  a  magnetic  field  set  up  between  them,  giving  induc- 
tive reactions.  The  coefficient  of  self-inductance  for  two 
wires  of  length  I  and  radius  a  at  an  axial  distance  b  apart  in 
air  is 


where  L  is  in  henries  ;  a,  b  and  I  in  centimetres  ;  and  n  the 
permeability  of  the  wire. 

The  self-inductance  of  a  thin  wire  is  greater  than  that  of 
a  thick  one  of  equal  length,  because,  for  equal  currents,  the 
strength  of  the  external  field  just  outside  the  periphery  is 
greater.  A  whisp  of  wires,  like  Fig.  224,  p.  389,  has  a  lesser 
self-inductance  than  a  single  wire  of  the  same  length,  and  a 
flat  strip  than  a  round  wire  of  equal  cross  section. 

For  a  long  tubular  coil  (without  iron)  of  length  I,  of  S 
turns,  each  of  area  A,  the  value  of  the  coefficient,  in  henries, 
is 


504.  Helmholtz's  Equation.  Time-constant.  —  From  that 
which  precedes  it  is  clear  that  whenever  a  current  is  turned 
on  there  is  a  variable  period  while  the  current  is  growing  up 
to  the  value  which  it  will  reach  when  steady,  namely  the 
value  as  determined  by  Ohm's  law.  During  the  variable 
period  Ohm's  law  does  not  apply. 

Von  Helmholtz,  who  investigated  mathematically  the 
effect  of  self-induction  upon  the  strength  of  a  current,  de- 
duced the  following  important  equations  to  express  the  rela- 


CH.  ix.  505]  GROWTH  OF  CURRENTS  483 

tion  between  the  inductance  of  a  circuit  and  the  time  required 
to  establish  the  current  at  full  strength :  — 

Let  dt  represent  a  very  short  interval  of  time,  and  let  the 
current  increase  during  that  short  interval  from  i  to  i  +  di. 
The  actual  increase  during  the  interval  is  di,  and  the  rate  of 
increase  in  strength  is  di/dt.  Hence,  if  the  inductance  be  L, 
the  electromotive-force  of  self-induction  will  be  —  Ui/dt, 
and,  if  the  whole  resistance  of  the  circuit  be  R,  the  strength 

of  the  opposing  extra-current  will  be  —  —  •  -j-  during  the  short 

R    dt 

interval  dt',  and  hence  the  actual  strength  of  current  flow- 
ing in  the  circuit  during  that  short  interval,  instead  of  being 
(as  by  Ohm's  law  it  would  be  if  the  current  were  steady) 
i  =  E/R,  will  be 

•  =  E_  L    di  =  dt 

R      R'  dt  R 

To  find  out  the  value  to  which  the  current  will  have  grown 
after  a  time  t  made  up  of  a  number  of  such  small  intervals 
added  together,  requires  an  application  of  the  integral  cal- 
culus, which  at  once  gives  the  following  result :  — 


/* 

(where  e  is  the  base  of  the  natural  logarithms,  2718). 

Put  into  words,  this  expression  amounts  to  saying  that 
after  a  lapse  of  t  seconds  the  self-inductance  in  a  circuit  at 
make  of  contact  has  the  effect  of  diminishing  the  strength  of  the 
current  by  a  quantity,  the  logarithm  of  whose  reciprocal  is  in- 
versely proportional  to  the  inductance,  and  directly  proportional 
to  the  resistance  of  the  circuit  and  to  the  time  that  has  elapsed 
since  closing  circuit. 

505.  The  Time-constant.  —  The  quantity  L/R,  the  re- 
ciprocal of  which  appears  in  the  exponential  expression,  is 
known  as  "  the  time-constant  "  or  "  persistence  "  of  the  cir- 
cuit. It  is  the  time  required  by  the  current  to  rise  to  a 


484 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  505 


certain  fraction,  namely  (e  —  !)/«  —  or  0-632  —  of  its  final 
value. 

A  very  brief  consideration  will  show  that  in  those  cases 
where  the  circuit  is  so  arranged  that  the  inductance  L  is 
small  as  compared  with  the  resistance  R,  so  that  the  time- 
constant  is  small,  the  term  (e~R'/L)  will  vanish  from  the 
equation  for  all  appreciable  values  of  t. 

On  the  other  hand  if  L  is  great  compared  with  R,  the 
current  during  its  growth  will  be  governed  almost  entirely 
by  the  inductance,  and  not  by  the  resistance  of  the  circuit, 
which  will  act  as  though  its  resistance  were  =  L/t. 


These  matters  are  graphically  depicted  in  Fig.  284,  in  which 
there  are  two  curves  of  rise  of  current.  Consider  a  circuit  having 
E  =  10  volts,  R  =  1  ohm,  L  =  10  henries.  The  time-constant  L/R 
will  be  10  seconds.  The  steady  current  will  be  10  amperes ;  it  starts 
off  as  if  it  intended  to  reach  the  top  value  at  the  end  of  the  time- 
constant;  but  at  the  end  of  1  second,  as  may  be  calculated  by 

Helmholtz's  equation,  the  current  is 
only  0*95  of  an  ampere.  In  2  seconds 
it  is  1-81,  in  5  seconds  3'95,  in  10 
seconds  6'34  amperes  (see  curve  A). 
At  the  end  of  a  whole  minute  it  is  only 
9-975  amperes.  Suppose  now  we  in- 
crease the  resistance  to  2  ohms,  and 
reduce  the  inductance  to  5  henries. 
The  final  value  of  the  current  will  be 
only  5  amperes  instead  of  10 ;  but  it 
will  rise  more  quickly  than  before  (see 
curve  B).  At  the  end  of  1  second  it  will 

be  1*647  amperes,  in  2  seconds  2755,  in  10  seconds  4'91  amperes.  We 
conclude  that  for  all  apparatus  that  is  required  to  be  rapid-acting 
(relays,  telephones,  chronographs,  etc.)  it  is  much  more  important 
to  keep  down  the  inductance  than  the  resistance  of  the  circuit. 
We  also  see  that  the  rule  (Art.  439)  so  often  given,  about  making 
the  resistance  of  a  battery  equal  to  that  of  the  rest  of  the  circuit, 
is  quite  wrong  for  cases  of  rapid  action.  If  the  circuit  has  self- 
inductance  as  well  as  resistance,  then  it  is  better  to  group  the  cells 
of  the  battery  so  as  to  have  higher  resistance,  namely  put  them  all 
in  series. 


0     2     4     6      8     IO    12    14    16    18  2O 

FIG.  284.  —  Curves  of  Growth 
of  Current. 


CH.  ix.  505]  EXTRA-CURRENT  485 

In  fact  everything  goes  on  as  though  at  time  t  after 
"  make  "  there  were  two  currents  flowing  in  opposite  direc- 
tions at  once;  one  the  ordinary  current  flowing  from  the 

first  at  full  strength,  the  other  the  extra-current  having  the 
-p 

value  —  —  e~m/L;    the   actual  current   being  the   difference 
K 

between  the  two. 

At  "  break  "  of  circuit  everything  goes  on  as  if,  the  ordi- 
nary current  having  dropped  suddenly  to  zero,  there  was 

TP 
superposed   an   extra-current  having  the  value  -f  —  e~R  /L ; 

XV 

but  here,  since  there  is  introduced  into  the  circuit  a  resist- 
ance of  unknown  amount  (the  resistance  along  a  spark  being 
indefinite)  the  calculation  becomes  impracticable.  We  know 
that  R  is  very  great ;  hence  we  know  that  the  variation  will 
be  more  sudden,  and  that  the  self -induced  E.M.F.  at  "  break  " 
is  much  greater  than  that  at  "  make." 

In  the  case  of  a  condenser  discharge,  CR  acts  in  the 
same  way  as  the  time-constant  L/R  does  in  the  case  of 
self-inductance. 

The  actual  quantity  of  electricity  conveyed  by  the  "  extra- 
current  "  is  equal  to  that  which  would  be  conveyed  by  cur- 
rent of  strength  E/R  lasting  for  time  L/R;  or  =  EL/R2. 
At  the  "  make  "  of  the  circuit  the  retardation  causes  the 
flow  of  electricity  to  be  lessened  by  the  amount  q  =  EL/R2. 
The  energy  which  is  stored  up  outside  the  wire  while  the 
current  grows  up  from  0  to  its  final  value  i  is  equal  to  J  <?E 


CHAPTER  X 

DYNAMOS,  ALTERNATORS,  AND  TRANSFORMERS 

LESSON   XLII.  —  Magneto-electric  and  Dynamo-electric  Gen- 
erators 

506.  Simple  Magneto-electric  Machines.  —  Faraday's  dis- 
covery of  the  induction  of  currents  in  conductors  by  mov- 
ing them  across  a  magnetic  field  suggested  the  construc- 
tion of  magneto-electric  machines  to  generate  currents  in 
place  of  voltaic  batteries,  and  Faraday  himself  constructed 
the  first  of  such  machines  (Fig.  147)  in  1831.  In  the  early 
attempts  of  Pixii  (1833),  Saxton,  and  Clarke,  bobbins  of 
insulated  wire  were  fixed  to  an  axis  and  spun  rapidly  in 
front  of  the  poles  of  strong  steel  magnets,  or  vice  versa.  In 
1856  Werner  Siemens  devised  an  improved  armature,  in 
which  the  coils  of  wire  were  wound  shuttle-wise  upon  a 
grooved  iron  core,  which  concentrated  the  magnetic  lines  in 
a  powerful  field  between  the  poles  of  a  series  of  adjacent  steel 
magnets. 

The  currents  thus  generated  by  the  rotating  coils  were 
necessarily  inverse  and  direct  currents  alternately,  since  the 
wires  moved  alternately  past  a  N-pole  and  a  S-pole.  In 
Figs.  285  and  286  the  wire  coil  is  supposed  to  be  spun  around 
a  longitudinal  axis,  the  upper  portion  coming  towards  the 
observer.  The  arrows  show  the  direction  of  the  induced 
currents  delivered  by  the  coils  to  the  circuit.  It  will  be  seen 
that  if  the  induced  E.M.F.  in  the  wires  as  they  move  past 
the  N-pole  towards  the  observer  is  from  left  to  right,  the 
two  slip-rings  will  alternately  become  +  and  —  at  each 
half-turn.  The  little  magneto-electric  machines,  still  sold 

486 


CH.  x.  507]      MAGNETO-ELECTRIC   MACHINES  487 

by  opticians,  and  the  magnetos  used  on  automobiles  for  pro- 
curing ignition,  are  on  this  principle. 

The  machine  then  consists  of  two  parts :  (1)  a  fixed  mag- 
net called  the  field  magnet;  and  (2)  a  rotating  coil,  or  system 
of  coils,  called  the  armature  1  in  which  electromotive-forces 
are  mechanically  generated  by  induction.  If  the  ends  of 
the  armature  coil  are  connected  as  in  Fig.  285  to  two  slip- 
rings  by  which  sliding  contact  is  made  with  the  external  cir- 


FIG.  285. —  Diagrammatic  Gener-  FIG.  286. —  Diagrammatic  Gener- 

ator (Alternating-current).  ator  (Continuous-current). 

cuit  the  machine  generates  alternating  currents,  and  is,  in 
fact,  an  alternator.  In  order  to  unite  these  reversed  impulses 
and  turn  the  successive  currents  into  one  direction,  it  was 
necessary  to  fix  upon  the  axis  a  commutator.  Fig.  286  illus- 
trates the  plan  adopted  by  Sturgeon  in  1836,  using  a  split 
tube  of  copper  to  commute  the  connexion  to  the  outer  circuit 
at  each  half-turn.  In  this  way  the  machine  becomes  a 
continuous-current  generator. 

There  are  therefore  two  classes  of  generators,  one  for  pro- 
ducing continuous  currents,  the  other  for  producing  alter- 
nating currents  (Art.  534). 

607.  Dynamo-electric  Machines.  —  The  name  dynamo- 
electric  machine,  or,  briefly,  dynamo,  is  given  to  any  machine 
for  converting  mechanical  power  into  electrical  power  by 
the  operation  of  producing  relative  motion  between  magnets 
and  conductors.  In  continuous-current  generators  the  part 

1  The  armature  of  a  generator  or  motor  is  that  part  of  the  machine 
which  consists  of  active  windings,  core  and  supports.  In  the  case  of  a 
generator  it  supplies  the  main  current  to  the  terminals ;  in  the  case  of  a 
motor  it  receives  the  main  current  from  the  terminals. 


488  ELECTRICITY  AND  MAGNETISM      [PT.  n.  507 

which  acts  as  magnet  and  is  termed  the  field-magnet  usually 
stands  still,  while  the  armature  revolves  between  its  poles. 
In  alternators  the  field-magnet  usually  revolves  within  a 
stationary  armature.  The  function  of  a  field-magnet  is  to 
provide  a  sufficiently  great  magnetic  flux.  The  armature, 
whether  it  revolves  or  stands  still,  is  the  part  in  which  the 
inductive  action  takes  place ;  the  copper  conductors  in  it 
cutting  the  magnetic  lines  of  the  flux.  In  the  early  machines 
the  field-magnets  were  either  permanent  magnets  of  steel  or 
else  electromagnets  independently  excited  by  means  of 
batteries.  The  next  improvement,  due  to  Sinsteden,  was 
to  excite  the  magnetism  of  the  field-magnets  by  means  of 
currents  furnished  by  a  little  magneto-electric  machine, 
known  as  the  exciter,  also  kept  in  rotation.  Various  sugges- 
tions were  made  by  Hjorth,  Murray,  S.  A.  Varley,  and  others 
to  render  the  machine  self-exciting  by  using  the  currents 
generated  in  the  armature  to  excite  the  field-magnets.  This 
was  done  in  1867  by  Varley,  Werner  Siemens,  and  Wheat- 
stone;  the  small  current  induced  by  the  feeble  residual 
magnetism  being  sent  around  the  electromagnet  to  exalt  its 
magnetism,  and  prepare  it  to  induce  still  stronger  currents. 
The  name  of  dynamo-electric  machines  was  at  one  time  given 
to  such  generators  to  distinguish  them  from  those  in  which 
permanent  steel  magnets  are  employed.  In  either  case  the 
current  is  due  to  magneto-electric  induction ;  and  in  either 
case  also  the  energy  of  the  currents  so  induced  is  derived 
from  the  dynamical  power  of  the  steam-engine  or  other 
motor  which  performs  the  work  of  moving  the  rotating  coils 
of  wire  in  the  magnetic  field.  So  the  name  has  been  extended 
to  all  generators,  whether  self-exciting  or  not.  In  all  of 
them  the  electromotive-force  generated  is  proportional  to 
the  number  of  turns  of  wire  in  the  rotating  armature,  and 
to  the  speed  of  revolution.  When  currents  of  small  electro- 
motive-force but  of  considerable  strength  are  required,  as 
for  electroplating,  the  rotating  armatures  of  a  generator 
must  be  made  with  small  internal  resistance,  and  therefore 


CH.  x.  508] 


DYNAMOS 


489 


of  a  few  turns  of  stout  wire  or  ribbon  or  rods  of  copper.  For 
producing  currents  at  a  high  electromotive-force  the  arma- 
ture must  consist  of  many  turns  of  wire  or  of  copper  conduc- 
tors suitably  connected. 

508.  Continuous  Current  Generators.  —  The  armatures 
of  modern  dynamos  are  complicated  structures  designed  to 
secure  continuity  of  action.  A  simple  coil,  such  as  Fig.  286, 
with  its  2-part  commutator  will  not  yield  a  steady  current ; 
for  twice  in  each  revolution  the  E.M.F.  dies  away  to  zero. 


FIG.  287.  —  Diagrammatic  Dynamo  with  Ring  Armature. 

The  coils  must  be  symmetrically  grouped  so  that  some  of 
them  are  always  active.  In  most  dynamos  the  armature 
winding  is  constructed  as  a  closed  coil,  the  wire  being  wound 
on  a  ring  core  of  iron  (Pacinotti's  core  with  teeth,  Gramme's 
core  without  teeth),  or  as  a  drum  over  a  cylindrical  core 
(Siemens's  or  Von  Hefner's  plan).  In  all  these  cases  the 
convolutions  are  joined  up  so  that  (like  the  ring  winding  in 
Fig.  287,  which  illustrates  a  simple  bipolar  design)  the  coil 
is  endless.  If  the  current  is  brought  in  at  one  side  of  such 
a  coil  and  taken  out  at  the  other  side  there  will  be  two  paths 
through  the  coil.  As  the  coil  spins  between  the  poles  of  the 
field-magnet  the  electromotive-forces  induced  in  the  ascend- 
ing and  descending  parts  will  tend  to  send  the  currents  in 
parallel  through  these  parts;  and  consequently  contact- 
brushes  must  be  set  to  take  off  the  currents  from  the  revolv- 


490  ELECTRICITY   AND   MAGNETISM     [PT.  n.  508 

ing  coils  at  the  proper  places.  The  brushes  are,  however, 
set  in  contact  not  with  the  coils  themselves  but  with  a  com- 
mutator, Fig.  288,  consisting  of  a  number  of  copper  bars, 
insulated  from  one  another,  and  joined  up  to  the  armature 
coil  at  regular  intervals.  Consider,  for  example,  a  Gramme 
ring  made  as  it  were  of  a  number  of  bobbins  wound  upon  a 
ring  core  of  iron.  Each  bobbin  constitutes  one  "  section  " 
of  the  winding,  and  they  are  all  joined  together,  the  end  of 
one  section  to  the  beginning  of  the  next,  and  each  such  junc- 
tion is  joined  down  to  a  bar  of  the 
commutator.  The  current  cannot 
pass  from  one  bar  of  the  commuta- 
tor to  the  next  without  traversing 
the  intervening  turns  of  the  wind- 
ings. The  commutator  revolves 
with  the  armature;  while  the 
brushes  which  convey  the  current 
to  and  from  the  circuit  are  clamped 
FIG.  288.  —  Commutator  and  in  suitable  holders  to  press  against 
its  surface  and  are  set  in  such  a 

position  that  the  current  passes  into  them  with  as  little 
sparking  as  possible.  As  the  current  in  each  turn  of  the 
armature  winding  must  be  reversed  in  direction  as  it  passes 
from  the  inductive  influence  of  one  pole  to  that  of  the  next 
pole  (and  in  thus  reversing  sets  up  reactive  electromotive- 
forces),  the  reversal  or  commutation  is  apt  to  be  delayed; 
with  the  consequent  production  of  sparks  between  the  com- 
mutator and  the  collecting  brushes.  To  prevent  sparking 
it  used  to  be  the  practice  to  set  the  brushes  a  little  in  advance 
of  the  diameter,  that  is  symmetrical  between  the  poles :  so 
that  each  section  of  the  winding,  as  it  passes  under  the  brush, 
is  at  that  instant  moving  in  a  magnetic  field  of  sufficient 
strength  to  generate  a  small  auxiliary  electromotive-force 
to  bring  about  a  quick  reversal.  In  many  modern  dynamos 
small  auxiliary  poles  are  fixed  between  the  principal  poles 
to  facilitate  sparkless  reversal.  The  current  in  the  armature 


CH.  x.  508] 


DYNAMOS 


491 


exercises  a  magnetizing  action,   and  tends  to  distort  the 
magnetic  field  in  the  direction  of  the  rotation,  interfering 


FIG.  289.  —  Bipolar  Dynamo. 

with  the  proper  magnetism  of  the  field-magnet.  The 
"  brushes  "  that  receive  the  current  were  originally  bunches 
of  springy  wires :  in  modern  machines  they  consist  of  small 
blocks  of  carbon,  or  are  built  up 
of  copper  strip  or  copper  gauze. 
Fig.  289  depicts  a  bipolar  type  of 
dynamo,  having  a  vertical  magnet 
of  massive  wrought  iron  magnetized 
by  currents  flowing  in  coils  wound 
upon  the  two  limbs.  Below,  be- 
tween the  polar  surfaces  which 
are  bored  out  to  receive  it,  is  the 
revolving  armature  (in  this  case  a 
drum-armature)  with  the  commu- 
tator and  brushes.  The  core  of  the  armature  is  built  up 
of  thin  iron  disks  (Fig.  290)  lightly  insulated  from  one  an- 
other, to  prevent  eddy-currents.  They  are  stamped  out  with 


FIG.  290.  —  Armature  Core-disk. 


492 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  509 


a  toothed  periphery.  When  assembled  on  the  shaft  the  slots 
between  the  teeth  form  channels  in  which  the  armature 
windings  are  secured.  Fig.  291  depicts  a  modern  armature. 


FIG.  291.  —  Drum-Armature. 

All  continuous-current   dynamos  will  run  as  motors   (Art. 
516),  if  supplied  with  current  at  the  proper  voltage. 

509.  Multipolar  Dynamos.  —  All  large  modern  genera- 
tors are  now  made  multipolar,  with  4,  6,  8,  or  more  poles; 
bipolars  being  used  in  small  sizes  only.  Fig.  292  depicts  a 
recent  4-pole  generator,  of  250  kilowatts  output,  running  at 


FIG.  292.  —  Modern  Four-pole  Dynamo. 


CH.  x.  510]  DYNAMO   CALCULATIONS  493 

375  revs,  per  minute,  delivering  500  amperes  at  500  volts. 
The  poles  are  alternately  North  and  South.  The  windings 
of  the  armature  consist  of  loops  which  span  across  a  chord 
about  equal  to  the  pole-pitch,  so  that  when  one  side  of  the 
loop  is  passing  a  N-pole,  the  other  shall  be  passing  a  S-pole. 
Successive  loops,  in  a  simple  drum  armature,  are  joined  up 
to  one  another  so  as  to  form  a  winding  that  is  re-entrant  as 
the  ring-winding  (Fig.  287)  is.  In  a  simple  drum  armature 
winding  such  as  this  (called  a  lap-winding)  there  will  be  the 
same  number  of  paths  (or  circuits  in  parallel)  through  the 
winding  as  the  machine  has  poles ;  and  there  must  be  the 
same  number  of  brushes  (or  rows  of  brushes)  spaced  out 
around  the  commutator.  In  another  and  less  simple  arrange- 
ment (called  a  wave-winding)  it  is  possible  to  have  the  num- 
ber of  circuits  or  paths  through  the  armature  different  from 
the  number  of  poles. 

510.  Dynamo  Calculations.  —  In  any  dynamo,  if  p  be  the 
number  of  poles,  c  the  number  of  paths  through  the  armature, 
g  the  magnetic  flux  passing  into  the  armature  at  one  pole 
(all  poles  being  numerically  equally  magnetized),  S  the  num- 
ber of  wires  or  conductors  around  the  armature  (counted  all 
round),  and  n  the  number  of  revolutions  per  second,  the 
electromotive-force  generated  by  the  revolving  armature  will 
be: 

E  =  2  x  wSg  -5-  108. 
c 

Or,  in  the  case  of  ring-wound  and  lap-wound  armatures, 
where  c  is  the  same  number  as  p,  the  formula  becomes 

E  =  nSg  -T-  108 ; 

since  the  number  of  magnetic  lines  cut  per  second  is  pro- 
portional to  each  of  the  three  quantities  n,  S,  and  ft;  and 
we  divide  by  108  to  bring  to  volts  (Art.  381,  p.  342). 

As  with  batteries  (Art.  205),  so  with  dynamos,  if  there  is 
an  internal  resistance  r,  the  available  volts  at  the  terminals 


494  ELECTRICITY   AND   MAGNETISM     [PT.  n.  510 

V  will  be  less  than  the  whole  volts  generated,  by  an  amount 
equal  to  ri,  the  lost  volts. 

V  =  E  -  ri. 

As  the  electrical  efficiency  of  the  machine  is  the  ratio  V/E, 
it  is  evident  that  r  should  be  as  low  as  possible. 

Example.  —  A  dynamo  having  $  =  7,170,000,  S  =  120,  running 
at  780  revs,  per  min.  (  =  13  revs,  per  sec.)  will  generate  an 
electromotive-force  of  111  volts.  If  r  =  0'033  ohm,  then 
when  i  =  210  amperes,  ri  =  7  volts.  Hence  V  =  104  volts. 

The  number  of  amperes  i  which  a  machine  is  supplying 
at  any  time  is  termed  its  load.  It  obviously  depends  on  the 
resistance  of  the  circuit  and  the  number  of  lamps  or  motors 
which  are  switched  on.  The  maximum  load  of  a  dynamo  is 
limited  by  the  heating  of  its  parts,  and  the  sparking  at  the 
brushes,  which  becomes  serious  if  too  large  a  current  is 
drawn  from  the  machine. 

The  output  of  a  dynamo  is  expressed  in  watts,  being  the 
number  of  amperes  multiplied  by  the  volts  at  terminals,  or 
iV;  or  in  kilowatts  (Art.  454)  as  iV  -r-  1000. 

The  efficiency  of  a  dynamo  is  the  ratio  between  the  out- 
put and  the  (mechanical)  input ;  the  input  being  the  power 
supplied  to  the  machine,  expressed  in  the  same  units. 

Example.  —  A  certain  dynamo  generating  110  volts  at  its 
terminals  is  found  when  giving  out  200  amperes  to  re- 
quire 32  H.P.  to  be  put  into  it  by  the  engine.  The  out- 
put is  22,000  watts.  The  input  is  32  X  746  =  23,872 
watts.  So  the  efficiency  is  22,000  -*-  23,872  =  0*92,  i.e. 
92  per  cent. 

The  causes  of  inefficiency,  that  is  the  sources  of  waste  of 
power,  in  a  dynamo,  are  as  follows : 

(i.)  Watts  lost  in  iron  of  armature,  caused  by  hysteresis 
and  eddy-currents  (Arts.  395  and  500). 

(ii.)  Watts  lost  in  excitation,  due  to  resistance  in  magnet 
coils  (Art.  461). 

(iii.)  Watts  lost  in  copper  of  armature,  due  to  resistance 
in  armature  windings  (Art.  461). 


CH.   X.  511] 


MODES   OF   EXCITATION 


495 


(iv.)  Watts  lost  in  friction,  etc.,  of  bearings  and  brushes. 

Of  these  (i.),  (ii.)»  and  (iv.)  are  nearly  constant  at  all 
loads;  while  (iii.)>  since  they  follow  the  i2r  law  (Art.  462, 
p.  442)  are  variable,  being  proportional  to  the  square  of  the 
load. 

All  the  armature  conductors  of  a  dynamo  are  subject, 
when  the  machine  is  running,  to  a  mechanical  drag  opposing 
the  rotation.  This  is  due  to  the  action  between  the  mag- 
netic field  and  the  current  (Art.  367). 

To  calculate  the  field-magnet  windings  the  formulse  of 
Arts.  405  and  431  must  be  applied  (see  p.  372  for  an  exercise 
on  windings). 

511.  Excitation  of  Field-Magnets.  —  There  are  several 
modes  of  exciting  the  magnetism  of  the  field-magnets,  giving 
rise  to  the  following  classification : 

1.  Magneto  Machine,  with  permanent  steel  magnets. 

2.  Separately  excited  Dynamo;   one  in  which  the  currents 
used  to  excite  the  field-magnets  are  furnished  by  a  separate 
machine  called  an  "  exciter." 


FIG.  293. 
Series-wound. 


FIG.  294. 
Shunt-wound. 


FIG.  295. 
Compound-wound. 


3.  Separate-coil  Dynamo,  with  a  separate  coil  wound  on 
the  armature  to  generate  the  exciting  current. 

4.  Series- Dynamo,  wherein  the  coils  of  the  field-magnet 
are  in  series  with  those  of  the  armature  and  the  external  cir- 
cuit (Fig.  293),  and  consist  of  a  few  turns  of  thick  wire. 

5.  Shunt-Dynamo,  in  which  the  coils  of  the  field-magnet 


496  ELECTRICITY  AND   MAGNETISM      [PT.  n.  512 

form  a  shunt  to  the  main  circuit ;  and,  being  made  of  many 
turns  of  thin  wire,  draw  off  only  a  small  fraction  of  the 
whole  current  (Fig.  294). 

6.  Compound-Dynamo,  partly  excited  by  shunt  coils, 
partly  by  series  coils  (Fig.  295). 

The  last  three  modes  are  illustrated  in  the  accompanying 
diagrams.  Each  variety  of  winding  has  certain  advantages 
depending  on  conditions  of  use. 

512.  Characteristic  Curves.  —  To  study  the  behaviour 
of  various  types  of  dynamo,  Hopkinson  devised  the  method 
of  characteristic  curves,  wherein  the  two  elements  of  output 
—  the  volts  and  the  amperes  —  are  plotted  out.  If  a  series- 
dynamo  is  examined  with  amperemeter  and  voltmeter, 
while  run  at  constant  speed  on  various  loads,  its  performance 
will  be  found  to  give  a  curve  like  AQV  in  Fig.  296,  where  the 
external  volts  are  plotted  vertically,  the  amperes  horizon- 
tally. This  curve  is  the  external 
characteristic.  The  volts  rise  as 
the  current  is  increased,  because 
of  the  increase  of  magnetization, 
but  when  this  is  near  saturation 
they  fall  again  because  of  internal 
resistance  and  sundry  reactions. 
At  any  point  such  as  Q  the  resist- 
°  M  ance  of  the  external  circuit  is  repre- 

FIG.   296.  —  Characteristic  Curves  -,   -,         ,-,          -,  ,.   ,,        v          r\r\ 

of  Series-Dynamo.  sented  by  the  slope  of  the  line  QO 

(i.e.  by  the  trigonometrical  tangent 

of  the  angle  QOX),  since  tan  QOX  is  equal  to  QM/OM 
(=  the  volts  divided  by  the  amperes).  If  line  OJ  be  drawn 
so  that  tan  JOX  is  equal  to  the  internal  resistance,  then  MN 
will  represent  the  lost  volts  when  the  current  =  OM.  Add- 
ing to  QM  a  piece  PQ  =  MN,  we  obtain  PM  as  the  corre- 
sponding value  of  the  total  electromotive-force.  In  this 
way,  from  the  curve  OV  we  can  construct  the  total  charac- 
teristic OE.  It  will  be  evident  that  if  the  total  resistance 
(i.e.  the  slope  of  the  line  OP)  be  increased,  P  will  come  down 


CH.  x.  513] 


CHARACTERISTIC   CURVES 


497 


the  curve  toward  O,  and  there  will  be  a  certain  point  at 
which  any  further  increase  in  the  slope  will  produce  a  sudden 
drop  of  volts  and  amperes  to  almost  zero.  This  is  a  pecu- 
liarity of  series  machines  ;  when  running  at  a  given  speed 
they  cease  to  yield  any  current  if  the  resistance  exceeds  a 
certain  critical  value,  depending  in  each  machine  on  its 
construction. 

For  a  shunt-dynamo  the  characteristic  has  a  different  form. 
When  the  machine  is  on  open  circuit,  giving  no  current  ex- 
ternally, the  shunt  circuit  is  fully  at  work  exciting  the 
magnet.  The  curve  YV  of  volts  at  terminals  begins  at  a 
high  value,  and  as  the  current  is  increased  by  diminishing 
the  resistance,  ike  voltage  gently  falls.  Part  of  this  drop 
is  due  to  internal  resistance  ;  part  is  due  to  armature  re- 
actions and  magnetic  distortion;  and  part  to  the  reduction 
of  the  shunt  current.  If,  as  be- 
fore, we  draw  OJ  to  represent  by 
its  slope  the  internal  resistance, 
we  can  find  the  lost  volts  MN  and 
add  these  on  above  Q,  so  obtain- 
ing P,  a  point  on  the  total  electro- 
motive-force curve,  YPE.  This 
also  droops  slightly.  If  a  shunt- 
dynamo  be  short-circuited,  its 


M 


magnetism  is  at  once  reduced  to    Fl0' 

almost  zero.     To  regulate  the  volt- 

age of  a  shunt-dynamo  a  suitable  rheostat  (Fig.  235)  may 

be   introduced   into   its   field-magnet   circuit,    to   vary   the 

exciting  current. 

513.  Constant  Voltage  Machines.  —  For  glow-lamp  light- 
ing, machines  are  needed  that  will  maintain  the  voltage 
constant,  whether  the  current  going  to  the  mains  be  small 
or  large.  The  current  that  flows  out  of  the  machine  will 
regulate  itself  exactly  in  proportion  to  the  demand;  more 
flowing  when  more  lamps  are  turned  on,  provided  the  poten- 
tial difference  between  the  mains  is  kept  constant.  For  this 

2K 


498        ELECTRICITY   AND   MAGNETISM     [PT.  n.  514,  515 

purpose  neither  a  series-dynamo  nor  a  shunt-dynamo  (driven 
at  a  constant  speed)  will  suffice ;  though  by  hand-regulation, 
as  above,  a  shunt-dynamo  may  be  used.  It  will  be  noted 
that,  while  in  shunt-machines  the  characteristic  drops  as 
the  current  is  increased,  in  series-machines  the  curve  rises. 
Consequently,  by  using  a  compound-winding,  consisting  of  a 
few  coils  of  thick  wire,  in  series  with  the  main  circuit  (to 
raise  the  excitation  in  proportion  to  the  load),  in  addition 
to  the  shunt  winding  (which  gives  the  proper  voltage  at  no- 
load),  the  voltage  may  be  kept  remarkably  constant.  By 
over-compounding  with  more  series  windings  the  dynamo 
may  be  made  to  maintain  a  constant  voltage  at  some  distant 
point  in  the  circuit  and  so  compensate  for  the  drop  in  voltage 
caused  by  the  resistance  of  the  cables. 

514.  Constant   Current   Machines.  —  Series   Lighting.  — 
To  maintain  an  unvarying  current  in  a  series  of  lamps,  as  is 
sometimes  wanted  for  lighting  with  arc  lamps  (Art.  486), 
special  dynamos  known  as  arc-lighting  machines  were  formerly 
used,  the  best  known  of  these  being  the  Brush  and  the 
Thomson-Houston    dynamos.     Both    had    open-coil    arma- 
tures (in  which  the  coils  are  not  grouped  in  a  closed  circuit), 
with  special  commutators,  and  automatic  devices  to  regu- 
late the  output,  the  one  by  shunting  the  exciting  current, 
the  other    by   shifting   the   brushes.      The    current    could 
thus  be  kept  at  10  amperes,  while  the  volts  change  (accord- 
ing to  the  number  of  lamps  in  circuit)   from  50  to  2000 
or  more. 

515.  Homopolar  Machines.  —  There  is  another  class  of 
dynamo-electric  machines,  differing  entirely  from  any  of  the 
preceding,   in   which   a   coil   or    other  movable   conductor 
slides  round  one  pole  of  a  magnet  and  cuts  the  magnetic  lines 
in  a  continuous  manner  without  any  reversals  in  the  direction 
of  the  induced  currents.     Such  machines,  sometimes  called 
"  unipolar  "  machines,  have,  however,  very  low  electromo- 
tive-force, and  are  not  practical.     Faraday's  disk-machine 
(Fig.  147)  belonged  to  this  class. 


CH.  x.  516] 


ELECTRIC   MOTORS 


499 


For  fuller  descriptions  of  dynamos,  and  technical  details 
of  construction,  the  reader  is  referred  to  the  author's  treatise 
on  Dynamo-electric  Machinery. 


LESSON  XLIII.  —  Electric  Motors  (Continuous  Current} 

516.  Electric  Motors.  —  An  electric  motor  is  a  species 
of  electromagnetic  engine,  that  is  to  say  a  machine  in  which 
the  motive  power -is  derived  from  electric  currents  by  means 
of  their  electromagnetic  action.  It  transforms  electrical 
energy  into  mechanical  work.  Faraday  (1821)  showed  a 
simple  case  (Art.  428)  of  rotation  produced  between  a  magnet 
"and  a  current  of  electricity.  Barlow  (1823)  produced  rota- 
tion in  a  star-wheel,  and  Sturgeon  in  a  copper  disk,  when 
traversed  radially  by  a  current  while  placed  between  the 
poles  of  a  horse-shoe  magnet.  Henry  (1831)  and  Ritchie 
(1833)  constructed  small  engines  producing  rotation  by  elec- 
tromagnetic means.  Fig.  298  shows 
a  modification  of  Ritchie's  motor. 
An  electromagnet  DC  is  poised  upon 
a  vertical  axis  between  the  poles  of  a 
fixed  magnet  (or  electromagnet)  SN. 
A  current,  generated  by  a  suitable 
battery,  is  carried  by  wires  which 
terminate  in  two  mercury-cups,  A, 
B,  into  which  dip  the  ends  of  the  coil 
of  the  movable  electromagnet  CD. 
When  a  current  traverses  the  coil 
of  CD  it  turns  so  as  to  set  itself  in 
the  line  between  the  poles  NS,  but 
as  it  swings  round,  the  wires  that  dip 
into  the  mercury-cups  pass  from  one 
cup  to  the  opposite,  so  that,  at  the 

moment  when  C  approaches  S,  the  current  in  CD  is  reversed, 
and  C  is  repelled  from  S  and  attracted  round  to  N,  the  cur- 
rent through  CD  being  thus  reversed  every  half  turn.  The 


FIG.  298.  —  Ritchie's  Motor. 


500  ELECTRICITY   AND   MAGNETISM     [PT.  n.  517 

mercury-cup  arrangement  was  superseded  by  the  commutator 
(Art.  508)  with  metallic  brushes  pressing  on  it. 

In  another  early  form  of  motor,  devised  by  Froment,  bars 
of  iron  fixed  upon  the  circumference  of  a  rotating  cylinder 
are  attracted  up  towards  an  electromagnet,  in  which  the  cur- 
rent is  automatically  broken  at  the  instant  when  each  bar 
has  come  close  up  to  its  poles.  In  a  third  kind,  an  electro- 
magnet is  made  to  attract  a  soft  iron  armature  up  and  down, 
with  a  motion  (like  the  piston  of  a  steam-engine)  which  is 
converted  by  a  crank  into  a  rotation.  In  these  cases  the 
difficulty  occurs  that,  as  the  attraction  of  an  electromagnet 
falls  off  rapidly  at  a  distance  from  its  poles,  the  attracting 
force  can  only  produce  effective  motion  through  very  small 
range.  Page  (1838-1850)  designed  various  motors,  in  some 
of  which  iron  plungers  were  sucked  into  hollow  tubular 
coils  of  wire  in  which  currents  were  caused  to  circulate  at 
recurring  intervals. 

Jacobi  (1839)  propelled  a  boat  along  the  river  Neva  at  the 
rate  of  2|  miles  per  hour  with  an  electromagnetic  engine 
of  about  one  horse-power,  worked  by  a  battery  of  64  large 
Grove's  cells. 

517.  Dynamo  as  Motor.  —  Daniel  Davis  appears  to  have 
been  the  first  to  recognize,  about  1842,  that  the  action  of  the 
electric  motor  is  the  simple  converse  of  that  of  the  dynamo 
or  generator.  Every  electric  generator,  such  as  is  used  in 
electric  lighting,  can  also  work  as  a  motor,  giving  out  mechan- 
ical power  when  supplied  with  electric  currents  from  some 
other  source.  Indeed  machines  designed  as  generators  make 
far  more  efficient  motors  than  any  of  the  older  sorts  of  elec- 
tromagnetic engines,  which  were  little  more  than  toys. 

Suppose  a  machine  designed  to  take  60  amperes  at  450 
volts,  in  other  words  a  27  kilowatt  machine.  Suppose  it  to 
be  such  that  the  inevitable  losses  (due  to  resistance,  hysteresis, 
etc.)  in  it  amount  to  10  per  cent,  or  2-7  kilowatts.  Then  if 
this  machine  is  used  as  a  generator  the  engine  must  supply 
it  with  power  to  the  amount. of  29-7  kilowatts,  which  is  39'8 


CH.  x.  518]  MOTORS  501 

H.P.  But  if  it  is  to  be  used  as  a  motor  and  only  27  kilowatts 
are  supplied  to  it  from  the  mains,  its  output  will  be  24-3 
kilowatts,  which  is  the  same  as  32-6  H.P.  (Art.  454). 

518.  Modern  Electric  Motors.  —  These  are  of  two  kinds  : 
(1)  those  for  use  with  continuous  currents  ;  (2)  those  for  use 
with  alternating  currents.  The  latter  are  considered  in  Art. 
547,  p.  530.  The  former  are  constructed  precisely  on  the 
plan  of  continuous  current  dynamos  (Art.  508)  having  fixed 
field  magnets  and  rotating  armature.  The  armature  is  dragged 
round  by  the  mutual  action  of  the  currents  flowing  in  the 
copper  conductors  and  the  magnetic  field  in  which  the  con- 
ductors lie.  As  explained  in  Art.  367,  the  force  acting  lat- 
erally on  the  conductors  is  proportional  to  the  product  of 
current  and  field.  Hence  if  very  powerful  field-magnets  are 
employed,  a  great  torque  (or  turning  moment)  can  be  pro- 
duced without  requiring  too  great  a  current  to  be  sent  into 
the  armature.  The  two  factors  of  mechanical  rotatory  power 
are  torque  (  =  angular  force)  and  angular  speed.  If  the  field 
of  the  motor  is  maintained  constant  the  torque  is  propor- 
tional to  the  current,  and  the  speed  is  proportional  to  the 
volts.  If  E  is  the  electromotive-force  generated  (in  direc- 
tion opposing  the  current,  see  Art.  455)  in  the  revolving 
armature,  and  i  the  current  supplied  to  the  armature,  the  elec- 
trical and  mechanical  expressions  for  the  power  (watts)  im- 
parted to  the  armature  are 

iE  =  anT, 

where  n  is  revolutions  per  second,  T  the  torque,  and  a  a  co- 
efficient depending  on  the  units  chosen.  If  n  is  expressed  in 
revolutions  per  second,  and  T  in  pound-feet,  the  value  of 
a  =  8  '52.  Now  in  a  revolving  armature  E  is  proportional 
(see  Art.  510)  to  p  the  number  of  poles,  to  S  the  number  of 
armature  conductors,  to  g  the  flux  per  pole,  and  inversely 
proportional  to  c  the  number  of  paths  through  the  windings. 

Hence 


8-52  c  108 


502 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  519 


Example.  —  A  4-pole  motor,  with  2  circuits  through  its  armature, 
with  a  flux  of  3,000,000  lines,  and  848  conductors  in  its  arma- 
ture, taking  70  amperes,  exerts  a  torque  of  420  pound-feet. 

If  the  armature  current  is  supplied  from  mains  at  con- 
stant voltage,  strengthening  the  magnetic  field  has  the 
effect  of  slowing  speed,  for  equal  power;  and  weakening 
the  field  quickens  the  speed.  Fig.  299  depicts  a  modern  con- 
tinuous-current motor 
of  90  horse-power,  de- 
signed to  run  at  600 
revolutions  per  minute 
when  supplied  with  90 
amperes  at  200  volts. 
Such  motors  are  made 
of  many  sizes  and 
forms.  Fig.  299  is  an 
open  motor,  but  many 
are  enclosed  to  keep 
out  dust;  and  if  in- 
tended for  use  in  mines 
must  be  totally  en- 
closed, i.e.  gas-tight. 
To  prevent  sparking 
at  the  commutator  it  is  usual  to  give  the  brushes"a  backward 
lead,  that  is  to  displace  them  a  little  in  the  opposite  direction 
to  that  of  the  rotation. 

519.  Efficiency  of  Motors.  —  If  an  ampere-meter  be  in- 
cluded in  the  circuit  with  a  battery  and  a  motor,  it  is  found 
that  the  current  is  weaker  when  the  motor  is  running  fast 
than  when  the  motor  is  running  slow  and  tunning  a  heavy 
load,  and  that  the  faster  the  motor  runs  the  weaker  does  the 
current  become.  This  is  due  to  the  E.M.F.  generated  in 
the  revolving  armature  of  the  motor,  which  necessarily  (Art. 
455)  opposes  the  current.  Applying  Ohm's  law  we  see  that 

.     V-E 


FIG.  299.  —  Continuous  Current  Motor  (open  type). 


CH.  x.  519]  EFFICIENCY   OF   MOTORS  503 

where  V  is  the  electromotive-force  supplied  by  battery  or 
dynamo,  E  the  back  electromotive-force  generated  by  the 
motor  as  it  runs,  and  R  the  resistance  of  the  circuit.  If 
the  magnetic  field  of  the  motor  is  of  constant  strength,  E 
will  increase  as  the  motor  gets  up  speed.  Consequently 
the  faster  it  runs  (or  the  stronger  its  field-magnet)  the  more 
is  the  current  diminished.  If  the  motor  only  exerts  a  small 
back  electromotive-force  it  cannot  utilize  much  of  the  power 
of  the  current.  If  V  be  the  volts  at  which  the  current  is  sup- 
plied, E  the  counter  electromotive-force  generated  by  the 
motor,  and  i  the  current,  then  Vi  =  gross  power  supplied, 
Ei  =  nett  power  utilized ;  and  dividing  the  latter  by  former 
we  get,  as  the  electrical  efficiency  of  the  motor,  the  ratio  E/V. 

Example.  —  Suppose  V  =  100   volts   and   E  =  90   volts,    the 
electrical  efficiency  will  be  90  per  cent. 

To  make  the  efficiency  as  high  as  possible  the  motor 
should  be  so  arranged  (either  by  strengthening  its  magnetic 
field,  or  by  letting  it  run  faster)  that  E  is  very  nearly  equal 
to  V.  In  that  case  the  motor  will  utilize  nearly  all  the  energy 
that  flows  to  it.  But  since,  by  Ohm's  law, 
the  current  is  =  (V  --  E)/r,  where  r  is  the 
internal  resistance  of  the  motor,  it  follows 
that  when  E  becomes  nearly  equal  to  V  the 
current  will  be  reduced  to  a  small  fraction 
of  what  it  would  be  if  the  motor  were  at 
rest.  The  diagram  (Fig.  300)  makes  the  O  L  X 

matter  plainer.  Let  the  line  OV  represent  FlG-  ^"^ ciency 
by  its  length  the  volts  of  supply  V,  and  let 
OE  represent  the  volts  generated  in  the  armature,  propor- 
tional to  speed  and  to  field.  On  OV  describe  the  square 
OVWX,  and  draw  the  diagonal  and  the  lines  EH,  KL.  Then 
the  area  EVWH  is  proportional  to  the  gross  power,  being 
V(V  —  E),  and  area  GLXH  is  proportional  to  the  nett  power 
utilized,  being  E(V  —  E).  These  two  areas  become  more 
nearly  equal,  though  both  become  small,  when  E  is  increased 


504         ELECTRICITY   AND   MAGNETISM    [PT.  n.  520,  521 

to  be  nearly  equal  to  V.  The  area  GLXH,  the  nett  power  of 
the  motor,  is  a  maximum  when  E  =  £  V ;  but  then  the  effi- 
ciency would  be  only  50  per  cent. 

520.  Starting   Resistances.  —  When   the   motor   is   only 
beginning  to  turn,  and  E  is  small,  the  current  would  be  enor- 
mous.    This  is  of  importance  in  the  starting  of  motors ;   for 
at  starting  the  great  rush  of  current,  which  would  certainly 
produce  an  enormous  torque,  would  destroy  the  armature 
by  overheating  it.     Hence  it  is  necessary  to  use  an  appli- 
ance called  a  starter,  which  is  an  arrangement  of  a  number 
of  graduated  resistances.     By  turning  a  handle,  a  consider- 
able amount  of  resistance  is  introduced  into  the  armature 
circuit  so  as  to  limit  the  rush  of  current  at  starting,  and  then 
this  resistance  is  gradually  cut  out  as  the  motor  acquires  its 
speed.     As  the  motor  speeds  up  it  generates  a  back  electro- 
motive-force  which   reduces   the   current   to   the   working 
strength  at  the  working  speed. 

521.  Excitation  and  Speed  of  Motors.  —  The  field-magnets 
of  motors  may  be  excited,  like  those  of  dynamos  (Art.  511). 
For  toys  and  small  machines  permanent  magnets  of  steel  may 
be  used.     In  larger  motors  electromagnets  are  employed, 
and  these  may  be  (i.)  separately  excited ;     (ii.)  excited  by 
connexion  in  series  with  the  armature ;  (iii.)  excited  in  shunt 
with  the  armature;    (iv.)  excited  in  both  shunt  and  series 
by  using  a  compound  winding.     Since  (Art.  510)  the  speed 
of  the  armature,  when  supplied  from  mains  at  a  constant 
voltage,  varies  inversely  as  the  strength  of  the  field,  it  follows 
that  in  shunt-wound  motors  the  speed  is  nearly  constant  at 
all  loads,  falling  off  a  little  as  the  load  increases  because  of 
internal  resistance.     But,  in  the  case  of  series-wound  motors, 
the  speed  falls  off  greatly  with  the  load,  for  at  large  loads  the 
current  increases  and  this  increases  the  magnetism,  bringing 
down  the  speed.     Uniform  speed  can  be  attained  by  using 
a  shunt  motor  having  a  few  series  turns  so  wound  as  to 
weaken  the  magnetism  as  the  load  increases. 

Hence  the  speed  of  motors  can  be  controlled  (a)  by  alter- 


CH.  x.  522]  ALTERNATING   CURRENTS  505 

ing  the  voltage  applied  to  the  motor;  (6)  by  putting  a 
rheostat  into  the  shunt  circuit  to  weaken  the  shunt  current, 
and  therefore  the  magnetism,  when  the  motor  is  required 
to  run  faster;  (c)  by  putting  into  the  path  of  the  current 
going  to  the  armature  a  resistance,  producing  a  drop  of  the 
voltage  available  for  the  armature  and  so  reducing  its  speed  ; 
but  this  expedient  wastes  energy.  Rheostats  to  vary  the 
speed  are  sometimes  combined  with  starters  (Art.  520)  so 
that  the  movements  of  a  handle  start  the  machine  and 
regulate  its  speed. 

LESSON  XLIV.  —  Alternating  Currents 

522.  Periodic  Currents.  —  We  have  seen  that  the  revolv- 
ing of  a  simple  coil  in  a  magnetic  field  sets  up  electromotive- 
forces,  which  change  in  direction  at  every  half-turn,  giving 
rise  to  alternating  currents.  In  each  whole  revolution  there 
will  be  an  electromotive-force  which  rises  to  a  maximum  and 
then  dies  away,  followed  immediately  by  a  reversed  electro- 
motive-force, which  also  grows  to  a  maximum  and  then  dies 
away.  Each  such  complete  set  of  operations  is  called  a 
cycle,  and  the  time  taken  for  one  cycle  is  called  a  period. 
The  number  of  periods  accomplished  in  a  second  is  called  the 
frequency  of  the  alternations,  and  is  denoted  by  the  letter  n. 
In  2-pole  machines  n  is  the  same  as  the  number  of  revolu- 
tions per  second ;  but  in  multipolar  machines  n  is  greater, 
in  proportion  to  the  number  of  pairs  of  poles.  Thus  a  ma- 
chine with  24  poles  driven  at  250  revolutions  per  minute 
will  work  with  a  frequency  of  50  periods  per  second ;  or,  in 
each  second  it  will  give  50  successive  to-and-fro  electro- 
motive impulses  or  waves.1  By  revolution  in  a  uniform  field 
the  electromotive-forces  set  up  are  proportional  to  the  sine 
of  the  angle  through  which  the  coil  has  turned  from  the  posi- 
tion in  which  it  lay  across  the  field.  If  in  this  position  the 

1  The  term  is  convenient,  but  these  alternating  impulses  are  not  strictly 
waves,  though  the  graphic  representations  of  them,  such  as  Fig.  301,  exhibit 
definite  wave-forms. 


506 


ELECTRICITY   AND   MAGNETISM      [PT.  n.  522 


flux  of  magnetic  lines  through  it  were  g,  and  the  number  of 
spirals  in  the  coil  that  enclose  the  g  lines  be  called  S,  then  the 
value  of  the  induced  electromotive-force  at  any  time  t  when 
the  coil  has  turned  through  angle  0  (=  2irnt  radians,  or 
=  360  nt  degrees)  will  be 

E«,  =  2  iroSg  sin  0  -*-  108, 
or,  writing  D  for  2  TrnSg/108,  we  have 
E,,  =  D  sin  0. 

In  actual  alternating  current  generators  (Art.  534)  the 
magnetic  fields  are  not  uniform,  nor  the  coils  simple  loops  ; 
so  the  periodic  rise  and  fall  of  the  electromotive-forces  will 
not  necessarily  follow  a  simple  sine  law.  The  form  of  the 
impressed  waves  depends  on  the  shape  of  the  polar  faces, 
and  on  the  form  and  breadth  of  the  coils.  But  in  most  cases 
we  are  sufficiently  justified  in  assuming  that  the  impressed 
electromotive-force  follows  a  sine  law,  so  that  the  value  at 
any  instant  may  be  expressed  in  the  above  form,  where  D 
is  the  maximum  value  or  amplitude  attained  by  E,  and  6  an 

angle  of  phase  upon 
an  imaginary  circle 
of  reference.  Con- 
sider a  point  P 
revolving  clockwise 
round  a  circle.  If 
the  radius  of  this 
circle  be  taken  as 
unity,  PN  will  be 
the  sine  of  the  angle  0,  as  measured  from  0°.  Let  the  circle 
be  divided  into  any  number  of  equal  angles,  and  let  the  sines 
be  drawn  similarly  for  each.  Then  let  these  sines  be  plotted 
out  at  equal  distances  apart  along  the  horizontal  line,  as  in 
Fig.  301,  giving  us  the  sine  curve,  which  is  a  smooth  wave-form. 
In  Fig.  301  one  revolution  of  P  around  the  circle  of  refer- 
ence corresponds  to  one  complete  cycle  of  changes.  The 
value  of  the  electromotive-force  (which  varies  between  +  D 


FIG.  301.  —  Curve  of  Sines,  showing  Wave-form  of 
Alternating  Electromotive-force. 


OH.  x.  523,  524     VIRTUAL   VOLTS   AND   AMPERES         507 

and  —  D  as  its  maximum  values)  may  be  represented  at  any 
moment  either  by  the  sine  PM  or  by  projecting  P  on  to  the 
vertical  diameter,  giving  OQ.  As  P  revolves,  the  point  Q 
will  oscillate  up  and  down  the  diameter. 

The  currents  which  result  from  these  periodic  or  alter- 
nating electromotive-forces  are  also  periodic  and  alternating ; 
they  increase  to  a  maximum,  then  die  away  and  reverse  in 
direction,  increase,  die  away,  and  then  reverse  back  again. 
If  the  electromotive-force  completes  50  such  cycles  in  a  second, 
so  also  will  the  current. 

523.  Virtual    Volts    and    Virtual    Amperes.  —  Measuring 
instruments  for  alternating  currents,  such  as  electrodyna- 
mometers  (Art.  425),  hot-wire  voltmeters  (Art.  465),  and  elec- 
trostatic voltmeters  (Art.  309),  do  not  measure  the  arithmet- 
ical average  values  of   the  amperes  or   volts.     If  these  in- 
struments are  first  calibrated  by  the  use  of  continuous  cur- 
rents, their  readings  will  be  the  square  roots  of  the  means 
of  the  squares  of  the  instantaneous  values.     They  measure 
what  are  called  virtual  amperes  or  virtual  volts.     The  mean 
which  they  read  (if  we  assume  the  currents  and  voltages  to 
follow  the  sine  law  of  variation)  is  equal  to  0-707  of  the 
maximum  values ;   for  the  average  of  the  squares  of  the  sine 
(taken  over  either  1  quadrant  OF  a  wrhole  circle)  is  J ;    hence 
the   square-root-of -mean-square    value   is    equal   to    1  -J-  V§ 
times  their  maximum  value.     If  a  voltmeter  is  placed  on  an 
alternating  circuit  in  which  the  volts  are  oscillating  between 
maxima  of  +  100  and  --  100  volts,  it  will  read  707  volts; 
and  70-7  volts  continuously  applied  would  be  required  to 
produce  an  equal  reading.     If  an  alternating-current  ampere- 
meter, or  electrodynamometer  (Art.  426),  reads  100  amperes, 
that  means  that  the  current  really  rises  to  +  141-4  amperes 
and  then   reverses   to  —  141  -4  amperes ;    but   the   effect  is 
equal  to  that  of  100  continuous  amperes,  and  therefore  such 
a  current  would  be  described  as  100  virtual  amperes. 

524.  Lag  and  Lead.  —  Alternating  currents  do  not  always 
keep  step  with  the  alternating  volts  impressed  upon  the  cir- 


508  ELECTRICITY   AND   MAGNETISM       [PT.  n.  525 

cuit.  If  there  is  self -inductance  (Art.  501)  in  the  circuit  the 
currents  will  lag :  if  there  is  capacity  (Art.  290)  in  the  circuit 
they  will  lead  in  phase.  Fig.  302  illustrates  the  lag  produced 
by  inductance.  The  impulses  of  current,  represented  by  the 
blacker  line,  occur  a  little  later  than  those  of  the  volts.  But 
inductance  has  another  effect  of  more  importance  than  any  re- 
tardation of  phase ;  it  produces  reactions  on  the  electromotive- 
force,  choking  the  current  down.  While  the  current  is  in- 
creasing in  strength  the  reactive  effect  of  inductance  tends  to 
prevent  it  rising.  To  produce  a  current  of  40  amperes  in  a 
resistance  of  1 J  ohms  would  require  —  for  continuous  cur- 

V 
/"\  I 

/  /\\       time_ 

XY7"  ''• 

FIG.  302.  —  Diagram  showing  Current  lagging  behind  Voltage. 

rents  —  an  E.M.F.  of  60  volts.  But  an  alternating  voltage 
of  60  volts  will  not  be  enough  if  there  is  inductance  in  the 
circuit  reacting  against  the  voltage.  The  matter  is  compli- 
cated by  the  circumstance  that  the  reactive  impulses  of  elec- 
tromotive-force are  also  out  of  step  :  they  are  in  fact  exactly 
a  quarter  period  behind  the  current. 

525.  Inductive  and  Non-inductive  Circuits.  —  Any  cir- 
cuit containing  self-inductance  is  described  as  an  inductive 
circuit,  as  distinguished  from  a  circuit  containing  resistance 
only,  which  is  termed  a  non-inductive  circuit.  In  an  inductive 
circuit  the  reaction  which  the  self-inductance  exerts  against 
any  change  in  the  strength  of  the  current  manifests  itself  as 
a  self -induced  electromotive-force.  If  an  alternating  cur- 
rent of  i  (virtual)  amperes  is  flowing  with  a  frequency  of  n 
periods  per  second  through  a  circuit  of  inductance  L,  the  re- 
active electromotive-force 1  will  be  2  irnLi  (virtual)  volts. 

'This  is  calculated  as  follows  (from  Art.  501),  E  =  Ldi/dt.  Now  i 
is  assumed  to  be  a  sine  function  of  the  time  having  instantaneous  value 
i0  sin  2  nut ;  where  i0  is  the  maximum  value  of  i.  Differentiating  this  with 


CH.  x.  525] 


INDUCTIVE    CIRCUITS 


509 


If,  for  example,  L  =  0-002  henry,  n  =  50  periods  per  second, 
and  i  =  40  amperes,  the  reactive  electromotive-force  will  be 
25-1  volts.  Now  if  we  wish  to  drive  the  40  (virtual)  amperes 
not  only  through  the  resistance  of  1J  ohms  but  also  against 
this  reaction,  we  shall  require  more  than  60  volts.  But  we 
shall  not  require  60  +  25-1  volts,  since  the  reaction  is  out  of 
step  with  the  current.  Ohm's  law  no  longer  meets  this 
condition.  To  find  out  what  volts  will  be  needed  we  have 
recourse  to  geometry. 

Plot  out  (Fig.  303)  the  wave-form  OAbd,  to  correspond 
to  the  volts  necessary  to  drive  the  current  through  .  the 
resistance,  if  there  were  no  inductance.  The  ordinate 
aA  may  be  taken  to  scale 
as  60.  This  we  may  call 
the  current  curve.  Then 
plot  out  the  curve  marked 
—  pLi  to  represent  the 
volts  needed  to  balance 
the  reaction  of  the  induc- 
tance. Here  p  is  written 
short  for  2  im.  The  or- 
dinate at  O  is  25-1;  and  the  curve  is  shifted  back  one 
quarter  of  the  period :  for  when  the  current  is  increasing 
at  its  greatest  rate,  as  at  0,  the  self-inductive  action  is 
greatest.  Then  compound  these  two  curves  by  adding 
their  ordinates,  and  we  get  the  dotted  curve,  with  its  maxi- 
mum at  V.  This  is  the  curve  of  the  volts  that  must  be  im- 
pressed on  the  circuit  in  order  to  produce  the  current.  It 
will  be  seen  that  the  current  curve  attains  its  maximum  a 
little  after  the  voltage  curve.  The  current  lags  in  phase 
behind  the  volts.  If  Od  is  the  time  of  one  complete  period, 
the  length  va  will  represent  the  time  that  elapses  between  the 
maxima  of  volts  and  amperes.  In  Fig.  304  the  same  facts 

respect  to  time  we  get  di/dt  =  2nni0  cos  2  nnt.  The  "virtual"  values  of 
cosine  and  sine  being  equal,  we  have  for  E  the  value  2  nnLi,  but  differing 
in  phase  from  the  current  by  one  quarter  of  a  period. 


FIG.  303. 


510  ELECTRICITY   AND   MAGNETISM      [PT.  n.  526 

are  represented  in  a  revolving  diagram  of  the  same  sort  as 
Fig.  301.  The  line  OA  represents  the  active  volts  R  X  i, 
whilst  the  line  AD  at  right  angles  to  OA  represents  the  re- 
active volts  pLii.  Compounding  these  as  by  the  triangle  of 
forces  we  have  as  the  impressed  volts  the  line  OD.  The 
projections  of  these  three  lines  on  a  vertical 
line  while  the  diagram  revolves  around 
the  centre  O,  give  the  instantaneous  values 
of  the  three  quantities.  The  angle  AOD, 
or  <£,  by  which  the  current  lags  behind  the 
impressed  volts,  is  termed  the  angle  of  lag. 
However  great  the  inductance  or  the  fre- 
quency, angle  <£  can  never  be  greater  than  90°.  If  OA  is  60 
and  AD  is  25-1,  OD  will  be  65  volts.  In  symbols,  the  im- 
pressed volts  will  have  to  be  such  that  E2  =  (R^)2  +  (pLi)2. 
This  gives  us  the  equation 

r-~-    E 

VR2  +  p2L2 

The  denominator  which  comes  in  here  is  commonly  called 
the  impedance,  and  the  product  pL  is  called  the  reactance. 

The  reciprocal  of  the  impedance  is  called  the  admittance. 
It  is  the  quotient  obtained  by  dividing  the  current  in  a 
circuit  by  the  electromotive-force  which  produces  it. 

526.  Maxwell's  Law.  —  In  Figs.  305. and  306  the  angle  of 
lag  is  seen  to  be  such  that  tan  <j>  =  pLi/~Ri  or  =  pL/R. 
And  it  is  evident  that  the 

.„  i«    ,  i        •      i  •  Impressed  Volts    *  Impedance 

effect  of  the  inductance  is    "^^"0  ; j  : 

to  make  the  circuit  act  as 
if  its  resistance  instead  of  FIG  305  FlG  306 

being  R  was  increased  to 

VR2  +  p2L2.  In  fact  the  alternating  current  is  governed  not 
by  the  resistance  of  the  circuit  but  by  its  impedance,  which 
is  the  conjoint  effect  of  resistance  and  reactance.  At  the 
same  time  the  current  is  lagging  as  if  the  angle  of  reference 
were  not  &  but  0  —  <t> ;  so  that  the  equation  for  the  instan- 
taneous values  of  i,  when  E  =  D  sin  0,  is 


CH.  x.  527,  528]  REACTANCE  511 

D  sin    9  ~  0 


VR2 

This  is  Maxwell's  law  for  periodic  currents  as  retarded 
by  self-inductance.  As  instruments  take  no  account  of 
phase,  but  give  virtual  values,  the  simpler  form  on  p.  510 
is  usually  sufficient. 

527.  Components  of  Current.  —  Instead  of  considering 
the  voltage  as  resolvable  into  two  components,  one  driving 
the  current  through  the  resistance,  the  other  driving  the 
current  against  the  reactance,  we  may  regard  the  matter 
in  another  way.  We  may  treat  the  current  as  capable  of 
being  resolved  into  two  component  currents  ;  one,  the  active 
current,  in  phase  with  the  voltage;  the  other,  the  reactive 
current  at  right  angles  in  phase  to  the  volt- 
age. If  we  write  ia  for  the  former,  and  im 
for  the  latter,  then  the  whole  current  i  will 
be  equal  to  V^Hj,  as  in  Fig.  307. 
Also,  ia  =  i  cos  <£;  and  im  =  i  sin  <£; 
where  <£,  the  angle  of  phase-difference  between  i  and  ia,  is 
the  angle  of  lag,  and  is  such  that  tan  <£  =  im/i.  The  in-phase 
component  is  called  the  active  component  because  it  is  the 
component  which  conveys  power.  The  reactive  component, 
also  sometimes  called  the  "  idle  "  or  "  watt-less  "  compo- 
nent, because  it  conveys  no  power  but  merely  reacts,  is  de- 
noted by  im  to  suggest  that  it  is  a  magnetizing  component. 

628.  Reactance  due  to  Capacity.  —  The  effect  of  capacity 
C  introduced  into  an  alternate  current  circuit  is  to  produce 
a  lead  in  phase,  since  the  reaction  of  a  condenser  instead  of 
tending  to  prolong  the  current  tends  to  drive  it  back.  The 
reactance  is  therefore  written  as  —  1/pC,  and  the  angle  <£ 
will  be  such  that  tan  <£  =  —  1/pCR.  The  impedance  will 
be  VR2  +  l/p2C2. 

If  both  self-inductance  and  capacity  are  present,  tan  <f> 
=  (pL  —  l/pC)/R;  the  reactance  will  be  pL  —  1/pC  ;  and 
the  impedance  VR2  +  (pL  -  1/pC)2. 


512         ELECTRICITY   AND   MAGNETISM     [PT.  n.  529,  530 

If  the  circuit  contain  no  inductance,  then  the  reactance 
present  will  be  that  due  to  the  capacity  alone.  Suppose  the 
current  to  be  led  through  a  circuit  of  but  small  resistance 

into  a  condenser  of  small 
capacity  (say  C  =  TV  mi- 
crofarad, then  1/pC  = 
10,000),  the  current  run- 
ning  in  and  out  of  the 

condenser  would  be  governed  only  by  the  capacity  and 
frequency,  and  not  by  the  resistance,  and  would  have  the 
value  — 

i  =  EpC. 

529.  Resonance.  —  Since  capacity  and  inductance  pro- 
duce opposite  effects  they  can  be  used  to  neutralize  one 
another.     They    exactly    balance    if    L  =  l/p2C.     In    that 
case  the  circuit  is  non-inductive  and  the  currents  obey  Ohm's 
simple  law,  and  the  strength  of  the  current  depends  on  the 
electromotive-force  and  the  resistance  only. 

Suppose  a  circuit  to  have  very  small  resistance  but  that 
it  has  both  capacity  and  inductance.  Then  it  follows  that 
if  in  that  circuit  we  impress  a  periodic  electromotive-force  of 
the  right  frequency  to  make  p  (i.e.  2  irri)  equal  to  1  -f-  VLC, 
there  will  be  a  very  large  alternating  current ;  for  at  that 
frequency  the  circuit  is  non-inductive,  and  the  inductive  re- 
actance pL  will  be  cancelled  by  the  capacitive  reactance 
1/pC.  But  if  the  frequency  is  higher  than  this,  pL  will  be 
greater  than  1/pC,  and  the  lagging  current  will  be  choked 
by  the  inductance ;  whereas  if  the  frequency  be  too  low  the 
capacitive  reactance  will  be  too  great  and  the  leading  current 
be  choked.  Hence  for  every  such  circuit  there  is  a  critical 
frequency,  n  =  1  -f-  2  TrVLC,  such  that  even  a  small  electro- 
motive-force of  that  frequency  may  set  up  a  large  current. 
This  is  the  phenomenon  of  electric  resonance.  (See  Art. 
602,  p.  608.) 

530.  Choking  Coils.  —  It  will  be  seen  that  if  in  a  circuit 
there  is  little  resistance,  and  much  reactance,  the  current 


CH.  x.  531]     ALTERNATING-CURRENT    POWER  513 

will  depend  on  the  reactance.  For  example  if  p(=  2  TTH) 
were,  say,  628  and  L  =  2  henries  while  R  was  only  1  ohm,  the 
resistance  part  of  the  impedance  would  be  relatively  negligible 
and  the  law  would  become 

.      E 

*~*T 

pL 

and  an  impressed  electromotive-force  of  1000  alternating 
volts  would  produce  less  than  1  ampere  in  that  circuit. 
Coils  with  large  self-inductance  and  small  resistance  are 
sometimes  used  to  impede  alternating  currents,  and  are 
called  choking  coils,  or  impedance  coils.  They  are  preferred 
to  rheostats  for  governing  alternating  currents,  because  they 
do  not  waste  power  (in  heat)  as  resistances  do.  If  the  iron 
core  is  made  movable,  so  that  the  inductance  can  be  varied 
by  moving  it  into  or  out  of  the  coil,  the  apparatus  can  be  used 
as  a  dimmer  to  lower  or  raise  the  brightness  of  lamps. 

531.  Alternating-current  Power.  —  If  to  measure  the 
power  supplied  to  a  motor,  or  other  part  of  an  alternating- 
current  circuit,  we  measure  separately  with  amperemeter 
and  voltmeter  the  amperes  and  volts,  and  then  multiply  to- 
gether the  readings,  we  obtain  as  the  apparent  watts  a  value 
often  greatly  in  excess  of  the  true  watts,  owing  to  the  differ- 
ence in  phase,  of  which  the  separate  instruments  take  no  ac- 
count. The  value  of  the  true  watts  divided  by  the  apparent 
watts  is  called  the  power-factor  and  is  expressed  as  a  decimal  or 
a  percentage.  The  true  power  (watts)  is  in  reality  the  prod- 
uct of  the  voltage  with  that  component  of  the  current  which 
is  in  phase  with  it.  Hence  W  =  iV  cos  <£ ;  where  i  and  V 
are  the  virtual  values,  and  <f>  the  angle  of  lag.  But  the  latter 
is  usually  an  unknown  quantity.  Hence  recourse  must  be 
had  to  a  suitable  watt-meter ;  the  usual  form  being  an  elec- 
trodynamometer  (Art.  458)  specially  constructed  so  that 
the  high-resistance  circuit  in  it  shall  be  non-inductive. 

Whenever  the  phase-difference  (whether  lag  or  lead)  is 
very  large,  the  current,  being  out  of  step  with  the  volts,  is 
almost  wattless.  This  is  the  case  with  currents  flowing  through 

2L 


514  ELECTRICITY   AND   MAGNETISM    [PT.  n.  532,  533 

a  choking-coil  or  into  a  condenser,  if  the  resistances  are 
small. 

532.  High   Frequency   Currents  :    Skin-Effect.  —  The  re- 
active effects   of   inductance   and  capacity  increase  if   the 
frequency  is  increased.     The  frequency  most  used  in  electric 
lighting  is  50  cycles  per  second.     If  high  frequencies  of  1000 
or  more  cycles  per  second  (see  Art.  603)  were  used  the  reac- 
tions would  be  excessive.     In  such  cases  the  currents  do  not 
flow  equably  through  the  cross-section  of  the  conducting 
wire,  but  are  confined  mainly  to  its  outer  surface;     even 
thick  rods  of  copper  offering  great  impedance.     At  a  fre- 
quency of  100  the  current  density  at  a  depth  of  12  millimetres 
from  the  surface  is  (in  copper)  only  about  \  of  its  value  in 
the  surface  layers.     In  iron  wires  the  depth  of  the  skin  for  \ 
value  is  about  1  millimetre.     This  phenomenon  is  known  as 
the  skin-effect.     It  is  proportional  to  the  conductivity  and 
permeability  of  the  wire,  and  to  the  frequency.     For  such 
rapid  oscillations  as  the  discharge  of  a  Ley  den  jar,  where  the 
frequency  is  several  millions,  the  conducting  skin  is  probably 
less  than  y^  of  a  millimetre  thick.      Hollow  tubes  in  such 
cases  conduct  just  as  well  as  solid  rods  of  the  same  outer  dia- 
meter ;  and  flat  metal  tapes  better  than  round  wires  of  equal 
weight.     The  conductance  is  proportional  not  to  section  but 
to  perimeter. 

Whenever  a  current  is  not  distributed  equably  in  the 
cross-section  of  any  conductor  there  is  a  real  increase  in  the 
resistance  it  offers  ;  the  heating  effect  being  a  minimum  when 
the  distribution  is  equal  all  through  the  cross-section.  The 
fact  that  the  oscillatory  currents  are  greatest  at  the  skin 
gives  the  strongest  support  to  the  modern  view  that  the  en- 
ergy in  an  electric  circuit  is  really  transmitted  by  the  sur- 
rounding medium  and  not  through  the  wire  (see  Art.  610 
on  energy  paths). 

533.  Alternating-current      Electromagnets.  —  When      an 
alternating  current  is  sent  through  a  coil  it  produces  an 
alternating  magnetic  field.     An  iron  core  placed  in  the  alter- 


CH.  x.  534] 


ALTERNATORS 


515 


nating  field  will  be  subjected  to  a  periodic  alternating  mag- 
netization. Electromagnets  for  alternating  currents  must 
have  their  iron  cores  laminated  to  prevent  eddy-currents ; 
and  the  coils,  owing  to  their  choking  action,  are  made  with 
fewer  turns  of  wire  than  if  designed  for  continuous  currents 
of  equal  voltage.  They  repel  sheets  of  copper  owing  to  the 
eddy-currents  which  they  set  up  in 
them ;  the  phase  of  these  eddy-currents 
being  retarded  by  their  self-induction. 
A  remarkable  illustration  is  afforded  by 
constructing  an  electromagnet  with  a 
long  core,  built  up  of  iron  strips,  pro- 
truding from  a  magnetizing  coil  (Fig. 
310).  If  a  ring  of  aluminium  is  loosely 
slipped  over  this  core,  and  an  alternat- 
ing current  is  switched  on  into  the  coil, 
the  ring  is  violently  repelled ;  and  may 
even  be  thrown  up  some  feet  into  the 
air.  The  currents  induced  in  the  ring 
are  in  opposite  directions  to  those  in 
the  coil,  and  hence  the  repulsion.  More- 
over the  currents  in  the  ring  tend  to 
oppose  the  alternations  of  the  flux  in 
the  core  and  drive  the  magnetic  lines  FlG-  31°-  —  Repulsion  due 

ill  ,  i     •,         Ti-iiii  to  Alternating  Currents. 

out  laterally  beneath  it.     If  held  down, 
the  ring  quickly  becomes  heated  by  the  induced  currents. 
Elihu  Thomson,  who  discovered  these  repulsions,  constructed 
some  motors  based  on  this  principle. 


LESSON  XLV.  —  Alternating  Current  Generators 

534.  Alternators.  —  The  simple  alternator  (Fig.  285),  with 
its  two  slip-rings  for  taking  off  the  current,  is  merely  diagram- 
matic. In  practice  machines  are  wanted  which  will  deliver 
their  currents  at  pressures  of  from  1000  to  10,000  volts, 
with  frequencies  of  from  15  to  50  cycles  per  second.  Lower 


516  ELECTRICITY  AND   MAGNETISM     [PT.  n.  534 

frequencies  than  about  40  are  unsuitable  for  lighting;  but 
they  are  preferred  for  motor-driving  and  transmission  of 
power.  High  voltages  are  common  with  alternating  currents 
because  of  the  economy  (Art.  551)  thereby  effected  in  the  cop- 
per mains.  Under  these  conditions  almost  all  alternators  are 
designed  as  multipolar  machines ;  and  since  the  perfect  in- 
sulation required  in  the  armatures  is  more  readily  attained 
if  these  parts  are  stationary,  it  is  usual  to  fix  them,  and  in- 
stead to  rotate  the  field-magnets.  One  advantage  of  alter- 
nators over  continuous-current  generators  is  that  there  is  no 
commutator,  and  no  sparking  at  any  collecting  brushes. 
There  are  two  principal  types  of  alternators :  — 
(i.)  Type  A.  —  Field-magnets  fixed  externally,  and  con- 
sisting of  a  number  of  poles,  alternately  N  and  S,  pointing 
radially  inwards;  armature  internal,  revolving,  consisting 
of  a  number  of  coils  embedded  in  slots  in  the  surface  of  a 
cylindrical  core  built  up  of  thin  iron  disks.  In  this  case  the 
currents  generated  in  the  armature  are  led  to  2,  3,  or  more 
slip-rings  fixed  on  the  shaft,  and  thence  to  the  circuit  through 
metal  brushes  which  make  sliding  contact  on  the  rings. 

(ii.)  Type  B.  —  Field-magnet  (or  rotor),  revolving  inter- 
nally, consisting  of  a  number  of  poles,  alternately  N  and  S, 
built  upon  a  foundation  wheel,  and  pointing  radially  outwards  ; 
armature  external,  fixed,  consisting  of  a  number  of  coils  em- 
bedded in  slots  or  tunnels  just  within  the  face  of  a  laminated 
iron  core.  Such  a  stationary  armature  is  called  a  stator. 
The  terminals  of  the  windings  on  the  stator  lead  directly 
to  the  mains  through  a  suitable  switchboard.  To  excite  the 
magnetism  of  the  revolving  field-magnet  or  magnet-field, 
continuous  currents  are  supplied  to  it  through  a  pair  of  slip- 
rings  fixed  on  the  shaft.  In  all  cases,  whether  the  magnets 
revolve  or  are  stationary,  the  exciting  current  is  supplied  from 
a  suitable  source,  usually  a  small  continuous-current  genera- 
tor called  an  exciter.  Since  one  whole  period  corresponds  to 
the  passage  of  a  pair  of  poles  N  and  S,  past  any  conductor, 
the  frequency  (i.e.  number  of  periods  per  second)  will  be  equal 


CH.  x.  534] 


ALTERNATORS 


517 


FIG.  311.  —  Magnet-wheel  of  an 
Alternator. 


to  the  number  of  pairs  of  poles  in  the  magnet-wheel  multiplied 
by  the  number  of  revolutions  per  second. 

When  driven  by  a  slow-speed  engine  or  water-turbine  the 
alternator  must  have  many  poles 
in  order  to  give  the  required  fre- 
quency of  alternations.  When 
driven  by  a  high  speed  steam- 
turbine  the  number  of  poles  is 
small,  usually  4  or  2.  For  a  fre- 
quency of  50  periods  per  second, 
a  2-pole  rotor  must  revolve  at 
3000  revolutions  per  minute ;  or  a 
4-pole  rotor  must  run  at  1500 
R.P.M. ;  or  one  with  8-poles  at 
750  R.P.M.,  etc.  Fig.  311  shows 
a  24-pole  magnet-wheel  belonging 
to  a  modern  alternator  of  800 
kilowatts  output,  to  be  driven  at  250  revolutions  per  minute, 
by  a  steam  engine  of  about  1120  horse-power.  Fig.  312  de- 
picts the  stationary  arma- 
ture of  a  larger  machine 
requiring  a  magnet-wheel 
with  36  poles,  designed  to 
run  at  200  revolutions  per 
minute,  giving  a  frequency 
of  60  periods  per  second." 
If  the  stator  of  an  alter- 
nator is  wound  with  but 
one  coil  or  group  of  coils 
opposite  each  pole  of  the 
magnet-wheel,  the  induc- 
tive action  in  each  coil  or 
group  as  the  poles  fly  past 
them  will  be  simultaneous, 
hence  the  coils  may  be  joined  up  in  one  single  circuit,  and 
the  (alternating)  electromotive-force  will  be  proportional  to 


FIG.  312.  —  Stator  of  an  Alternator. 


518  ELECTRICITY   AND   MAGNETISM     [PT.  n.  535 

the  number  of  coils  so  joined  up.  A  single  coil  or  loop  may 
be  regarded  as  composed  of  two  conductors ;  and  if  the  whole 
number  of  conductors  so  joined  together  be  called  Z,  the 
number  of  loops  or  coils  will  be  J  Z.  If  the  flux  from  any  one 
pole  of  the  magnet-wheel  (all  poles  being  supposed  to  be 
equally  strong)  be  denoted  by  g,  and  if  the  frequency  is  called 
n,  then  the  generated  electromotive-force  E  expressed  in 
virtual  volts  is  given  by  the  formula 

E=/cXnXZxg-^108; 

where  A;  is  a  coefficient  of  value  from  2  to  2-22,  depending 
on  the  shape  of  the  poles  and  the  distribution  of  the  coils 
in  the  slots.  A  machine  with  only  one  such  circuit  on  the 
stator  windings  is  called  a  single-phase  alternator. 

Example.  —  A  certain  20-pole  alternator  having  a  flux  of 
1,750,000  lines  per  pole,  has  a  coil  of  24  turns  opposite  each 
pole.  It  revolves  at  300  revolutions  per  minute.  Assume 
k  =  2*16.  Here  n  =  50,  because  10  pairs  of  poles  pass 
each  coil  5  times  per  second ;  and  Z  =  960  because  the 
total  number  of  turns  in  series  is  480.  Hence  by  the 
formula  E  =  1814'4  volts. 

635.  Two-phase  and  Three-phase  Alternators.  —  If  the 
stator  of  an  alternator  is  wound  with  two  (or  three)  inde- 
pendent similar  windings  which  are  displaced  with  respect 
to  one  another  so  that  the  inductive  actions  on  the  different 
sets  of  windings  are  not  simultaneous,  there  will  be  a  differ- 
*ence  of  phase  (Art.  524)  between  the  electromotive-forces 
induced  in  them.  Two-phase  alternators  are  those  in  which 
the  second  set  of  windings  is  displaced  by  half  a  pole-pitch 
with  respect  to  the  first  set ;  and  the  respective  electromotive- 
forces  will  consequently  differ  by  a  quarter  of  one  period. 
They  furnish  two  separate  alternating  currents.  Three- 
phase  alternators  have  three  separate  sets  of  similar  windings, 
displaced  from  one  another  by  two-thirds  of  a  pole-pitch, 
so  that  there  will  be  three  electromotive-forces  generated,  of 
equal  amplitude,  but  differing  in  phase  from  one  another 
by  one-third  of  a  period.  Such  machines,  furnishing 


CH.  x.  536] 


TURBO-ALTERNATORS 


519 


three  alternating  currents,  are  the  most  usual  kind  of  al- 
ternator, since  the  three-phase  system  is  best  adapted  for  the 
transmission  of  power.  Three  lines  only,  not  six,  are  re- 
quired to  convey  the  three  currents ;  because  if  one  end  of 
each  of  the  three  windings  is  brought  to  a  common  junction, 
and  the  other  three  ends  are  joined  respectively  to  the  three 
lines,  no  other  return  line  is  needed  ;  each  line  serving  in  suc- 
cession as  a  return  for  the  currents  in  the  other  lines.  How 
this  occurs  is  understood  from  the  diagram  of  Fig.  313,  which 


FIG.  313.  —  The  Three  Currents  of  a  Three-phase  System. 

shows  three  successive  equal  alternating  currents,  A,  B,  C, 
properly  spaced  out  at  equal  intervals  of  time.  It  will  be 
noticed  that  at  the  moment  when  any  one  is  at  its  positive 
maximum  value  the  other  two  are  each  of  half-value  and 
negative :  and  that  at  the  moment  when  any  one  is  at  zero- 
value,  the  other  two  are  at  86-6  of  the  maximum,  one  positive, 
one  negative.  When  the  three  circuits  are  joined  as  de- 
scribed the  value  of  the  volts  between  the  lines  is  equal  to 
V3  times  that  of  the  volts  generated  in  any  one  of  the  three 
windings. 

536.  Turbo-Alternators.  —  For  use  with  steam-turbines 
a  special  type  of  alternator  has  been  evolved.  The  high  speed 
necessitates  few  poles,  and  a  most  solid  and  symmetrical 
construction  of  the  rotor.  This  is  usually  constructed  as  a 
steel  cylinder,  devoid  of  projecting  poles,  but  in  which  the 
magnetic  poles  are  formed  by  inserting  in  deep  slots  the  copper 
windings  wherein  the  exciting  current  is  caused  to  circulate. 


520 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  536 


Fig.  314  shows  the  unwound  core  of  the  rotor  of  the  largest 
turbo-alternator  yet  made,  of  25,000  kilowatts  output,  re- 
quiring about  33,000  horse-power  to  drive  it,  constructed  by 

Messrs.  Parsons  of 
Newcastle  for  the 
Commonwealth  Com- 
pany of  Chicago.  The 
diameter  of  this  core 
is  74  inches  and  its 
length  130J  inches  :  it 
weighs  about  50  tons ; 
and  has  4  poles.  The 
stator  of  this  machine 
is  depicted  in  Fig. 
315.  The  diameter 
of  the  bore  is  75  inches,  and  there  are  84  slots  each  enclosing 
one  copper  conductor.  The  complete  stator  weighs  about 
100  tons.  The  machine  revolving  at  750  revolutions  per 


FIG.  314.  —  Rotor  of  Parsons's  Turbo-alternator  of 
25,000  Kilowatts  Output. 


FIG.  315.  —  Stator  of  Parsons's  Turbo-alternator  of  25,000  Kilowatts  Output. 


CH.  x.  537]        COUPLING   OF  ALTERNATORS  521 

minute  furnishes  3  alternating  currents  of  about  3200  amperes 
each,  at  4500  volts  between  the  terminals,  at  a  frequency  of 
25  periods  per  second. 

537.  Coupling  of  Alternators.  —  In  the  use  of  two  or 
more  alternators  on  one  circuit  a  peculiarity  arises  that  does 
not  exist  with  continuous-current  dyna- 
mos, owing  to  differences  of  phase  in  the 
currents.  If  two  alternators  driven  by 
separate  engines  are  running  at  the  same 
speed  and  at  equal  voltage,  it  will  not  do 
to  join  their  circuits  by  merely  switching 
them  to  the  mains  if  they  are  not  also 
in  phase  with  one  another;  or  serious  FIG.  316. -TDiagram  of 
trouble  may  occur.  In  central  station  Alternators  in  Parallel, 
work  it  is  usual  to  run  several  machines  all  in  parallel.  Now 
if  two  machines  are  feeding  into  the  same  mains  each  is  tend- 
ing to  send  current  back  to  the  other ;  and  if  their  electro- 
motive-forces are  at  any  instant  unequal,  that  with  the 
greater  will  tend  to  send  its  current  the  opposite  way  through 
the  other.  To  explain  what  occurs  consider  Fig.  316,  which 
is  a  revolving  diagram  of  the  same  kind  as  Figs.  301  and  304. 
If  the  two  alternators  are  exactly  in  step  they  will  both  be 
sending  a  pulse  of  current  toward  the  mains  at  the  same 
moment,  but,  so  far  as  the  circuit  connecting  them  is  con- 
cerned, these  impulses  will  be  exactly  opposed.  Let  OA  and 
OB  represent  these  two  exactly-opposed  impulses.  Now 
suppose  one  of  the  two  machines  to  gain  a  little  on  the  other, 
OA  shifting  forward  to  OA'.  The  two  electromotive-forces 
no  longer  balance,  but  will  have  a  resultant  OE  tending  to 
make  a  current  oscillate  through  the  two  machines,  this 
current  being  out  of  phase  both  with  the  leading  machine  A 
and  with  the  lagging  machine  B.  But  this  local  current 
will  itself  lag  a  little  in  phase  behind  OE  because  of  the  induc- 
tance in  its  path.  Let  the  phase  of  the  current  then  be  indi- 
cated by  OC,  which  is  set  back  a  little.  There  is  now  a  cur- 
rent surging  to  and  fro  between  the  two  machines,  and  it  is 


522  ELECTRICITY   AND   MAGNETISM      [FT.  n.  538 

obviously  more  nearly  in  phase  with  OA  than  with  OB.  This 
means  that  in  the  leading  machine  A  the  volts  and  amperes 
are  more  nearly  in  phase  with  one  another  than  in  the  lag- 
ging machine  B.  Reference  to  Arts.  455  and  519  will  at  once 
show  that  the  current  is  helping  to  drive  B  as  a  motor,  and  that 
a  greater  mechanical  effort  will  be  thrown  on  A,  which  is 
acting  more  as  a  generator.  Hence  this  interchange  of  cur- 
rent tends  automatically  to  bring  up  the  lagging  machine 
and  to  load  the  leading  machine.  They  will  come  back  into 
phase.  All  alternators  of  good  construction  suitably 
driven  will  run  together  in  parallel,  even  though  their 
electromotive-forces  are  unequal.  On  the  other  hand,  if 
two  alternators  are  joined  in  series,  the  resulting  current, 
when  they  are  ever  so  little  out  of  phase,  tends  to  load  the 
lagging  machine  and  hasten  the  leading  one  till  they  get 
into  complete  opposition  of  phase,  one  running  entirely  as 
generator,  the  other  entirely  as  motor.  This  is  excellent 
for  transmission  of  power  from  an  alternator  at  one  end 
of  a  line  to  a  synchronous  alternator  at  the  other : 
the  two  machines  keep  step  at  all  loads.  But  they  will 
not  run  together  in  series  if  both  are  to  act  as  generators, 
unless  rigidly  coupled  together  on  the  same  shaft. 

To  prevent  accidents  arising  from  too  sudden  a  transfer 
of  current  between  two  machines  it  is  usual  in  lighting 
stations  to  employ  a  synchronizer,  a  device  to  indicate  the 
phases  of  the  alternations.  When  an  alternator  is  to  be 
switched  into  circuit  (in  parallel  with  one  or  more  others) 
the  operator  does  not  put  the  switch  in  until  (speed  and  volts 
being  both  right)  the  electromotive-force  of  the  machine  has 
come  exactly  into  identical  phase  with  that  of  the  circuit  into 
which  it  is  to  be  introduced. 


LESSON  XL VI.  —  Transformers  and  Converters 

538.    Alternating-Current    Transformers.  —  Transformers 
are  needed  in  the  distribution  of  currents  to  a  distance,  be- 


CH.  x.  538]  TRANSFORMERS  523 

cause  glow-lamps  in  the  houses  need  low  pressures  of  50  to 
100  or  200  volts,  whilst  for  economy  of  copper  in  the  mains 
it  is  necessary  (see  Art.  551)  that  the  generators  should  work 
at  high  pressures  of  1000  to  5000  or  more  volts.  The  prin- 
ciple of  transformation  was  briefly  touched  in  Art.  245. 
Alternating-current  transformers  are  simply  induction-coils 
having  well-laminated  iron  cores,  usually  of  thin,  soft  sheet- 
iron  strips  piled  together,  and  shaped  so  as  to  constitute  a 
closed  magnetic  circuit.  Upon  the  cores  are  wound  the 
primary  coil  to  receive  the  alternating  current,  and  a  second- 
ary coil  to  give  out  other  alternating  currents.  As  the 
transformer  is  generally  required  to  reduce  the  pressure  from 
high  to  low,  the  primary  usually  consists  of  many  turns  of 
fine  copper  wire,  very  well  insulated,  to  receive  a  small 
current  at  high  pressure ;  and  the  secondary  of  a  few  turns 
of  thick  copper  wire  or  ribbon,  to  give  out  a  much  larger 
current  at  low  pressure. 

To  transform  down  from  about  2000  volts  to  100  volts, 
the  ratio  of  the  windings,  called  the  ratio  of  transformation, 
will  be  20 :  1.  Whatever  the  ratio  of  the  voltages,  the  cur- 
rents will  be  about  in  the  inverse  ratio,  since,  apart  from  the 
inevitable  small  losses  in  transformation,  the  power  put  in 
and  taken  out  will  be  equal.  Taking  the  above  case  of  a 
transformer  having  20 :  1  as  the  ratio  of  its  windings,  if  we 
desire  to  take  out  of  the  secondary  300  amperes  at  100  volts, 
we  must  put  into  the 
primary  at  least  15 
amperes  at  2000 

, .  Alternator 

volts.  _^^_^_^___^_-_ 

In     Scattered      dis-  Lou>  Pressure  Mains 

trictS    a    Small    trans-       FlG>  317<  ~~  Transformers  in  a  Distributing  System. 

former  is  provided  for  each  house,  the  lamps  being  in  the 
low  pressure  circuit.  In  cities  large  transformers  are  placed 
in  substations,  from  which  issue  the  low-pressure  mains  dis- 
tributing the  current  to  the  houses.  Fig.  317  shows  in  dia- 
gram the  simple  use  of  transformers  on  a  distributing  system. 


524        ELECTRICITY   AND   MAGNETISM    [PT.  n.  539,  540 

539.  Energy    Relations.  —  It    is    clearly    impossible    to 
take  out  from  the  secondary  of  a  transformer  more  power 
than  is  being  supplied  to  the  primary  coils.     In  the  above 
example  15  amperes  are  being  supplied  at  2000  volts,  that 
is  30,000  watts  are  being  supplied  to  the  primary,  therefore 
the  secondary,  working  at  1000  volts,  could  not  give  out  more 
than  300  amperes  at  100  volts,  at  the  most.     There  are  in- 
evitable losses  of  energy  in  the  transformer  itself  owing  to 
the  internal  resistance  of  the  copper  coils  and  to  the  waste  of 
power  by  hysteresis  and  eddy-currents  (Arts.  395  and  500) 
in  the  iron.     Suppose  these  losses  amount  to  1 J  per  cent,  then 
if  we  are  to  take  300  amperes  from  the  secondary,  the  primary 
will  need  not  15  but  15-225  amperes.     But  it  will  actually 
take  in  a  little  more  than  this  because  a  small  additional  mag- 
netizing current  is  required  to  magnetize  the   iron    core. 
Even  at  times  of  no-load,  when  no  current  is  being  taken  from 
the  secondary  windings  there  will  be  a  small  magnetizing 
current  in  the  primary.     In  the  above  example  of  a  30- 
kilowatt  transformer,  the  no-load  magnetizing  current  would 
probably  amount  to  about  half  an  ampere. 

540.  Construction  of  Transformers.  —  The  iron  cores  are 
always  built  up  of  thin  sheets  of  soft  iron.     Figs.  318  and 


FIG.  318.  —  Transformer  with  FIG.  319.  —  Transformer  with 

Concentric  Coils.  Sandwiched  Coils. 

319  show  a  simple  pattern.  Both  sets  of  windings,  primary 
and  secondary,  are  wound  in  coils  that  surround  the  two 
limbs.  Sometimes  the  primary  and  secondary  coils  are 
wound  as  concentric  cylinders  that  slip  one  inside  the  other, 
as  in  Fig.  318,  sometimes  as  ring  coils  sandwiched  between 
one  another  as  in  Fig.  319.  In  either  case  the  primary  coils 


CH.  x.  541] 


MODERN   TRANSFORMERS 


525 


FIG.  320.  —  Transformer 
with  Divided  Magnetic 
Circuit. 


must  be  most  carefully  insulated  from  one  another,  and 
from  the  core.  In  another  common  form  the  core  is  con- 
structed as  in  Fig.  320,  with  the  P  and  S  coils  surrounding 
a  single  core,  while  the  outer  parts  of  the 
iron  stampings  complete  the  magnetic 
circuits. 

It  is  most  important  in  transformers 
that  the  whole  of  the  magnetic  lines 
created  by  the  currents  in  one  of  the 
coils  should  pass  through  the  interior  of 
the  other  coils  :  in  other  words,  that  there 
should  be  no  magnetic  leakage.  Hence 
all  gaps  or  joints  in  the  iron  of  the  mag- 
netic circuit  should  be  as  far  as  possible  avoided,  and 
the  two  sets  of  coils  should  be  as  close  to  one  another 
as  is  consistent  with  good  insulation.  Fig.  321  shows  a 

small  transformer  manu- 
factured by  Messrs.  Fer- 
ranti,  having  terminals  in- 
sulated on  porcelain  sup- 
ports at  the  tops. 

Large  transformers  for 
lighting  and  power  trans- 
mission are  usually  im- 
mersed in  oil  tanks  to  pre- 
serve good  insulation  and 
promote  cooling. 

For  three-phase  working 
(Art.  535),  a  transformer 
is  needed  having  three 
primary  and  three  second- 
ary coils,  wound  on  three 
Or  three  separate  transformers  may  be 


FIG.  321.  —  A  Small  Modern  Transformer. 


connected  cores, 
used. 

541.    Elementary  Theory  of  Transformers.  —  If  the  pri- 
mary volts  are  maintained  constant,  the  secondary  volts  will 


526  ELECTRICITY  AND  MAGNETISM      [PT.  n.  541 

be  nearly  constant  also,  and  the  apparatus  becomes  beauti- 
fully self-regulating,  more  current  flowing  of  itself  into  the 
primary  when  more  lamps  are  turned  on  in  the  secondary 
circuit.  This  arises  from  the  choking  effect  of  self-induction 
in  the  primary.  If  no  lamps  are  on  the  secondary  circuit  the 
primary  coil  simply  acts  as  a  choking-coil.  When  all  the 
lamps  are  on,  the  primary  acts  as  a  working-coil  to  induce 
currents  in  the  secondary.  When  only  half  the  lamps  are 
on,  the  primary  acts  partly  as  a  choking-coil  and  partly  as  a 
working-coil. 

Let  Vi  be  the  volts  at  the  primary  terminals,  ¥2  those  at 
the  secondary  terminals  ;  Si  the  number  of  turns  in  the  pri- 
mary coil,  82  the  number  in  the  secondary  ;  r\  the  internal 
resistance  in  the  primary,  r2  that  of  the  secondary.  Call 
the  ratio  of  transformation  k  =  Si/S2.  The'  alternations  of 
magnetism  in  the  core  will  set  up  in  the  two  coils  electromo- 
tive-forces EI  and  E2  strictly  proportional  to  their  respective 
numbers  of  turns  (if  there  is  no  magnetic  leakage)  ; 

Ei  =  444rcSig-^-  108; 
E2  =  444nS2g  -^  108; 

so  E2  =  Ei/fc  ;  and  since  (apart  from  magnetizing  and  hys- 
teresis effects  which  necessitate  a  small  addition  to  the 
primary  current)  EI^I  =  E2^2,  it  follows  that  ii  =  iz/k. 
The  volts  lost  in  the  primary  are  rtf'i,  those  in  the  secondary 
r2i2.  Hence  we  may  write 

Vi  =  E!  +  nil, 
V2  =  E2  -  rsi* 

Writing  the  first  as  Ei  =  Vi  —  r^'i  =  Vi  —  r&z/k,  and 
inserting  Ei/fc  for  E2  in  the  second  equation,  we  get 


which  shows  that  everything  goes  on  in  the  secondary  as 
though  the  primary  had  been  removed,  and  we  had  substi- 
tuted for  Vi  a  fraction  of  it  in  proportion  to  the  windings, 


CH.  x.  542]    INDUCTANCE  IN  TRANSFORMERS  527 

and  at  the  same  time  had  added  to  the  internal  resistance  an 
amount  equal  to  the  internal  resistance  of  the  primary,  re- 
duced in  proportion  to  the  square  of  the  ratio  of  the  windings. 
We  also  see  that  to  keep  the  secondary  volts  constant  the 
primary  generator  must  be  so  regulated  as  to  cause  the  pri- 
mary volts  to  rise  slightly  when  much  current  is  being  used 
in  the  secondary  circuit.  The  currents  in  the  two  coils 
are  in  almost  exact  opposition  of  phase;  they  reach  their 
maxima  at  the  same  instant,  flowing  in  opposite  senses  round 
the  core.  The  efficiency  of  well-constructed  transformers 
is  very  high  (98  per  cent,  or  more),  the  internal  losses  being  a 
very  small  percentage  of  the  working  load. 

542.  Self-inductance  and  Mutual  Inductance  in  Trans- 
formers. —  It  is  obvious  that  each  of  the  two  coils  of  a  trans- 
former, if  considered  by  itself,  possesses  a  coefficient  of  self- 
inductance  (Art.  501).  Let  the  self-inductance  of  the  pri- 
mary by  itself  be  called  LI,  and  that  of  the  secondary  by  itself 
be  called  L2.  When  they  are  considered  as  working  together 
there  will  be  a  coefficient  of  mutual  inductance  M  between 
them  (Art.  497) .  We  have  seen  (Art.  497)  that  if  two  coils,  of 
Si  and  S2  turns  respectively,  are  wound  around  the  same  core 
M  =  SiS2/Z.  From  Art.  501  we  see  that  the  respective  coef- 
ficients of  self -inductance  will  be  LI  =  Si2/Z,  and  L2  =  S22/Z, 
So,  if  there  is  no  magnetic  leakage,'  M  =  VLiL2 ;  and  LI 

=  &M,  and  L2  =  -M.     And  the  effect  when  the  transformer 
k 

is  supplying  the  load  is  that  the  mutual  inductance  neutralizes 
the  effect  of  the  self-inductance  in  both  circuits.  But  if 
there  is  any  magnetic  leakage  M  will  be  less  than  VLiL2, 
leaving  uncompensated  part  of  the  self-inductances  of  the 
circuits,  so  that  in  each  of  them  there  is  some  choking  action. 
Moreover,  when  the  secondary  is  only  partly  loaded  its  cur- 
rent neutralizes  part  only  of  the  self -inductance  of  the  primary, 
which  therefore  automatically  chokes  off  a  part  of  the  current 
that  would  otherwise  flow  in  from  the  primary  mains.  In 
fact,  the  effective  self-inductance  of  the  primary  when  the 


528        ELECTRICITY   AND   MAGNETISM      [PT.  n.  543,  544 

transformer  is  at  work  is  equal  to  LI  —  M— •     At  full-load 

*i 

iz/ii  is  nearly  equal  to  k,  so  that  the  primary  self-inductance 
is  almost  neutralized.  At  no-load,  when  iz  =  0,  the  primary 
current  is  choked  down  by  the  self -inductance  LI  to  a  mere 
dribble  of  magnetizing  current.  As  a  result,  the  flow  of  pri- 
mary current  from  the  primary  mains  automatically  adjusts 
itself  to  the  requirements  of  the  load  on  the  secondary  cir- 
cuit. 

543.  Coupling  of   Circuits   by   a   Transformer.  —  If   the 
transformer  is  arranged  so  that  in  neither  circuit  there  is 
any  uncompensated   self-inductance,   so   that  M  =  VLiL2, 
circuits  are  said  to  be  tight-coupled;    this  is  the  case  only 
when  there  is  no  magnetic  leakage,  so  that  all  the  lines 
of  flux  interlink  with  both  circuits.     But  if  the  transformer 
is  such  that  a  considerable  proportion  of  the  magnetic  lines 
due  to  current  in  either  circuit  fail  to  interlink  themselves 
with  the  other  circuit,  M  will   be  much  less  than  VLiL2, 
and  the   circuits  are  said   to  be   loose-coupled.     The  effect 
of  loose-coupling  can   be  produced   either   by  keeping  the 
primary  windings  far  away  from  the  secondary  windings,  or 
by  adding  separate  self-inductance  to  either  or  both  of  the 
circuits.     The  degree  of  coupling  is  expressed  by  the  formula 
c  =  M  -T-  VLiL2 ;   c  being  called  the  coefficient  of  coupling. 

544.  The  Problem  of  Conversion.     Motor-generators.  — 
To  convert  an  electric  current  of  one  species  into  an  electric 
current  of  another  species  is  a  problem  that  presents  itself 
in  many  different  forms.     The  general  solution  of  the  problem 
is  to  set  the  current  of  one  species  to  run  a  motor  that  me- 
chanically drives  a  generator  supplying  current  of  the  other 
species.     Such  a  group  of  two  coupled  machines  is  called  a 
motor-generator.     In  this  way  an  alternating  current  may  be 
converted  into  a  continuous  current  by  using  an  alternating 
motor  coupled  to  a  continuous-current  generator.     Or  a  two- 
phase  alternating  current  may  be  converted  into  a  three- 
phase  alternating  current.     Or  an  alternating  current  of  a 


CH.  x.  545,  546]  CONVERTERS  529 

given  frequency  may  be  converted  into  another  alternating 
current  of  a  different  frequency  by  the  use  of  two  coupled 
alternators  having  different  numbers  of  poles,  this  arrange- 
ment being  called  a  frequency-changer.  In  all  these  cases  it 
is  the  electrical  energy  which  is  mechanically  transferred 
from  one  machine  to  another. 

545.  Continuous-current  Converters.  —  To  convert  con- 
tinuous currents  from  one  voltage  to  another  it  is  necessary 
to  employ  a  rotating  apparatus,  which  is  virtually  a  motor- 
generator.     For  example,  a  motor  receiving  a  current  of  10 
amperes  at  1000  volts  may  be  made  to  drive  a  dynamo  giving 
out  nearly  200  amperes  at  50  volts.     Instead  of  using  two 
separate  machines,  one  single  armature  may  be  wound  with 
two  windings  and  furnished  with  two   commutators;    the 
number  of  turns  in  the  windings  being  proportioned  to  the 
voltages,  and  their  sectional  areas  to  the  amperes.     One 
field-magnet  suffices.     The  elementary  theory  of  these  is  the 
same  as  that  in  Art.  541,  EI  and  E2  now  standing  for  the  elec- 
tromotive-forces respectively  induced  in  the  two  windings 
on  the  revolving  armature. 

546.  Rotatory  Converters,  or  Synchronous  Converters.  — 
Revolving  machinery  equivalent  to  a  combination  of  an 
alternating  motor  and  continuous- 
current  dynamo  may  be  used  to 

transform  alternating  currents  into 
continuous,  or  vice  versa.  In  this 
case  also  two  separate  machines 
need  not  always  be  used.  Fig.  322 
represents  in  diagram  an  elemen-  FIG.  322.  -  Diagram  of 
tary  rotatory  converter  having  both  Converter, 

a  simple  commutator  to  collect  continuous  currents,  and  a 
pair  of  slip-rings  for  alternating  currents.  Such  a  machine 
may  convert  continuous  currents  into  alternating,  or  alter- 
nating into  continuous.  Or  it  may  act  as  a  motor  if  supplied 
with  either  kind  of  current ;  or  may,  if  driven  mechanically, 
generate  both  kinds  of  current  at  the  same  time. 

2M 


530  ELECTRICITY  AND   MAGNETISM     [PT.  n.  547 

The  rotatory  converters  of  commerce,  of  which  Fig.  323  is 
an  example,  have  armatures  wound  exactly  like  those  of 
ordinary  continuous  current  dynamos,  with  the  usual  wind- 
ings and  commutator.  But  at  the  other  end  of  the  shaft 
they  are  provided  with  a  set  of  slip-rings,  3,  4,  6,  or  more  in 
number,  connected  symmetrically  to  appropriate  points  on 
the  winding,  to  suit  the  alternating  currents  with  which  they 


FIG.  323.  —  A  Small  Rotatory  Converter. 

have  to  deal.  If  supplied  through  the  slip-rings  with  alter- 
nating current  they  run  as  synchronous  motors  (Art.  547) 
and  generate  continuous  currents  which  are  taken  off  by  the 
brushes  at  the  commutator.  The  field-magnets  are  excited 
either  separately  or  by  taking  a  fraction  of  the  current  from 
the  continuous-current  side. 


LESSON  XL VII.  —  Alternating-current  Motors 

547.  Synchronous  Motors.  —  We  have  seen  (Art.  537) 
that  one  alternator  can  drive  another  as  a  motor,  the  two 
machines  in  series  working  in  synchronism.  There  are  two 


CH.  x.  548]  ALTERNATING   MOTORS  531 

disadvantages  in  such  motors  —  (i.)  that  they  are  not  self- 
starting,  but  must  be  brought  up  to  speed  before  the  current 
is  applied;  (ii.)  that  their  field-magnets  must  be  separately 
excited  with  continuous  currents.  Other  forms  of  motor 
have  consequently  been  sought.  Ordinary  continuous- 
current  motors,  if  made  with  laminated  iron  magnets,  will 
work,  though  not  well,  with  alternating  currents. 

548.  Polyphase  Currents.  —  We  have  seen  that  alternators 
can  be  designed  to  generate  two,  or  three,  alternating  cur- 
rents of  equal  frequency  but  differing  iA 
from  one  another  in  phase.  We  have  now 
to  see  how,  if  two  equal  alternate  currents, 
differing  in  phase  by  one-quarter  of  a  * 
period,  are  properly  combined,  they  can 
be  made  to  produce  a  rotatory  magnetic 
field.  And  in  such  a  rotatory  field  con- 
ductors can  be  set  rotating,  as  was  first  FIQ.  324.— Two-phase 
suggested  by  Baily  in  1879.  Consider 
an  ordinary  Gramme  ring  (Fig.  324)  wound  with  a  contin- 
uous winding.  If  a  single  alternating  current  were  intro- 
duced at  the  points  AA'  it  would  set  up  an  oscillatory  mag- 
netic field,  a  N-pole  growing  at  A,  and  a  S-pole  at  A',  then 
dying  away  and  reversing  in  direction.  Similarly,  if  another 
alternate  current  were  introduced  at  BB',  it  would  produce 
another  oscillatory  magnetic  field  in  the  BB'  diameter.  If 
both  these  currents  are  set  to  work  but  timed  so  that  the  BB' 
current  is  J  period  behind  the  AA'  current,  then  they  will 
combine  to  produce  a  rotatory  magnetic  field,  though  the  coil 
itself  stands  still.  This  is  quite  analogous  to  the  well-known 
way  in  which  a  uniform  rotatory  motion,  without  any  dead 
points,  can  be  produced  from  two  oscillatory  motions  by  using 
two  cranks  at  right  angles  to  one  another,  the  impulses  being 
given  J  period  one  after  the  other.  The  above  combination 
is  called  a  two-phase  system  of  currents.  If  the  BB'  current 
is  J  period  later  than  the  AA'  current,  the  rotation  in  Fig. 
324  will  be  clockwise.  Another  way  of  generating  a  rotatory 


532  ELECTRICITY   AND   MAGNETISM     [PT.  n.  549 

field  is  by  a  three-phase  system l  (Art.  535)  of  currents. 
Let  three  alternating  currents,  differing  from  one  another  by 
J  period  (or  120°),  be  led  into  the  ring  at  the  points  ABC. 
The  current  flows  in  first  at  A  (and  out  by  B  and  C),  then 
at  B  (flowing  out  by  C  and  A),  then  at  C  (out  by  A  and  V), 
again  producing  a  revolving  magnetic  field.  This  is  anal- 
ogous to  a  3-crank  engine,  with  the  cranks  set  at  120°  apart. 
There  are  several  ways  of  combining  the  circuits  that 
receive  the  currents  of  the  various  phases.  For  example, 
the  windings  of  Fig.  324  might  be  divided  into  four  separate 
coils,  each  having  one  end  joined  to  a 
common  junction,  and  the  four  outer  ends 
joined  respectively  to  the  four  line  wires. 
Or  the  windings  of  Fig.  325  might  be 
arranged  as  three  separate  coils,  each 
having  one  end  joined  to  a  common  junc- 

tion»  aild  ™ih  the  thre6  Outer  6Ilds  J°ilied 

respectively  to  the  three  line  wires.  Such 
arrangements  would  be  called  star  groupings,  as  distinguished 
from  the  mesh  groupings  of  the  cuts.  Also  the  coils,  in 
whichever  way  grouped,  need  not  be  wound  upon  a  ring. 
The  two-phase  coils  of  Fig.  324  might  be  wound  upon  four 
inwardly-projecting  pole-pieces;  and  the  three-phase  coils 
of  Fig.  325  might  be  wound  upon  three  inwardly-projecting 
pole-pieces.  Or  in  larger  multipolar  machines  a  three-phase 
set  of  coils  might  be  arranged  upon  a  set  of  six,  nine,  twelve, 
or  more  projections,  in  regular  succession,  or  be  embedded 
in  slots  exactly  as  in  the  stators  of  alternators. 

549.  Induction  Motors.  —  In  such  rotating  magnetic 
fields  any  pivoted  masses  of  metal  at  once  begin  to  rotate, 
and  will  acquire  a  speed  a  little  less  than  the  speed  at  which 
the  invisible  field  revolves.  In  such  a  centred  mass,  or  rotor, 
eddy-currents  are  set  up  (just  as  in  Arago's  rotations,  Art. 
500),  which  drag  the  metal  mass  and  tend  to  turn  it.  The 

1  Three-phase  currents  on  a  large  scale  were  first  used  in  the  famous 
Frankfort  transmission  of  power  in  1891.  See  Art.  551. 


CH.  x.  549]  INDUCTION  MOTORS  533 

strength  of  these  currents  in  the  rotating  part  depends  on  the 
relative  speed  of  the  field  and  the  rotor.  If  the  rotor  were 
to  revolve  with  speed  equal  to  the  revolving  field,  the  eddy- 
currents  would  die  away,  and  there  would  be  no  driving  force. 
The  difference  between  the  speed  of  the  field  and  the  speed 
of  the  rotor  is  called  the  slip.  At  full  load  the  slip  does  not 
usually  exceed  3  or  4  per  cent  of  the  synchronous  speed. 
The  rotor  actually  used  in  such  motors  consists  of  a  cylindri- 
cal core  built  up  of  thin  iron  disks,  over  which  is  built  up  a 
sort  of  squirrel  cage  of  copper  rods  joined  together  at  their 
ends  into  a  closed  circuit.  The  rods  are  inserted  in  slots  or 


FIG.  326.  —  A  small  Induction  Motor,  showing  Stator  and  Rotor. 

hojes  just  below  the  surface  of  the  core.  The  rotor  need  not 
have  any  commutator  or  slip-rings,  and  is  entirely  discon- 
nected from  any  other  circuit.  It  receives  its  currents  wholly 
by  induction.  In  some  forms  the  rotor  is  wound  with  coils 
like  a  drum  armature,  and  the  coils  are  connected  through 
slip-rings  to  enable  resistance  to  be  inserted  in  the  circuits  of 
the  windings  at  starting,  and  cut  out  as  the  rotor  gets  up  its 
speed.  Such  induction  motors  or  asynchronous  motors  start 
with  considerable  torque  (or  turning  moment)  and  have  a 
high  efficiency  on  full  load.  Similar  motors  for  single-phase 
alternating  currents  are  now  in  extensive  use.  To  procure 
the  necessary  difference  of  phase  at  starting,  the  alternating 
current  must  be  split  into  two  currents  differing  in  phase. 


534  ELECTRICITY  AND   MAGNETISM     [PT.  n.  550 

This  is  done  by  the  use  of  a  divided  circuit,  in  the  two  branches 
of  which  different  reactances  are  introduced.  If  in  one 
branch  there  is  a  choking-coil  to  offer  inductance,  the  cur- 
rent in  that  branch  will  be  retarded.  If  in  the  other  there  is 
a  condenser,  the  current  in  this  branch  will  be  advanced  in 
phase.  Or  if  a  plain  resistance  is  used  in  that  branch  the 
current  in  it  will  be  less  retarded  in  phase.  Combining 
these  two  currents  a  rotatory  field  is  produced  for  starting 
the  movement.  When  once  the  motor  has  started  a  further 
turn  of  the  switch  simply  puts  on  the  alternating  current, 
as  at  AA'  in  Fig.  324,  and  it  continues  to  be  driven,  though 
the  impulse  is  now  only  oscillatory. 

550.  Commutator  Motors.  —  In  recent  years  alternating 
motors,  both  three-phase  and  single-phase,  have  been  intro- 
duced, consisting  of  a  stator,  similar  to  those  already  de- 
scribed, to  which  the  currents  are  supplied,  and  a  rotor  that 
is  furnished,  like  the  drum  armature  of  an  ordinary  dynamo, 
with  a  commutator  and  sets  of  brushes.  In  some  cases  the 
rotor  circuits  are  in  series  with  those  of  the  stator,  in  other 
cases  in  shunt,  or  in  some  cases  they  are  short-circuited. 
Motors  of  this  class  have  the  advantage  that  they  can  be 
adjusted  so  as  not  to  lower  the  power-factor  of  the  circuit, 
as  induction  motors  are  liable  to  do. 

The  field-magnets  must  be  built  up  of  thin  laminations  or 
stampings  of  thin  sheet-iron  or  mild  steel. 


CHAPTER  XI 

TRANSMISSION   AND   DISTRIBUTION   OF   POWER 

LESSON  XL VIII.  —  Electric  Transmission  of  Power 

551.  Transmission  of  Power  from  Generator  to  Motor.  — 
Power  may  be  transmitted  to  great  distances  electrically 
from  a  generator  at  one  end  of  the  circuit  to  a  motor  at  the 
other.  A  mountain  stream  may  be  made  to  turn  a  turbine 
which  drives  a  dynamo  or  alternator,  the  currents  from 
which  are  conveyed  to  some  centre  of  population  by  insu- 
lated wires  to  motors  which  reconvert  the  electrical  power 
into  mechanical  power.  Electric  transmission  on  the  large 
scale  may  be  said  to  date  from  1891  by  the  striking  demon- 
stration at  Frankfort,  in  which  140  horse-power  was  conveyed 
from  the  Falls  of  the  Neckar  at  Lauffen,  117  miles  away, 
through  three  wires  only  4  millimetres  in  diameter,  with  a 
nett  efficiency  of  74  per  cent,  including  all  losses.  This  was 
followed  by  the  erection  of  the  first  great  power  station  at 
Niagara.  Since  that  date  power  stations  have  been  erected 
in  all  quarters  of  the  world,  in  Switzerland,  Lombardy, 
Norway,  Sweden,  the  United  States,  and  Canada;  in  fact 
wherever  large  waterfalls  are  available.  Millions  of  horse- 
power have  thus  been  utilized  for  driving  factories,  for  light- 
ing, and  for  electrochemical  processes. 

Fig.  327  illustrates  the  case  of  a  simple  transmission  be- 
tween two  machines  using  continuous  current.  In  one  the 
electromotive-force  drives  the  current,  in  the  other  the 
electromotive-force  opposes  the  current.  The  first  acts  as 
generator  (by  the  principle  of  Art.  455),  the  second  as  motor. 
If  their  respective  electromotive-forces  are  EI  and  E2  the 
electrical  efficiency  of  the  transmission  is  the  ratio  E2/Ei. 

The  power  lost  in  the  line  by  reason  of  its  resistance  is 
the  chief  difficulty  to  face  in  such  transmissions,  owing  to 

535 


536 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  551 


the  prohibitive  price  of  copper  for  carrying  large  currents 
without  overheating.  The  watts  wasted  in  a  line  of  resist- 
ance R  (Art.  459)  are  =  ??R.  The  gross  watts  utilized  are 
(Art.  454)  =  ^VM,  where  VM  is  the  volts  at  the  motor  end. 
Hence  the  power  that  must  be  generated  at  the  sending  end 
of  the  line  is  £2R  -f  iVM  watts.  Now  it  will  be  obvious  that 


GENERATOR  MOTOR 

FIG.  327.  —  Elementary  Diagram  of  Electric  Transmission  of  Power. 

one  may  keep  the  ??R  loss  constant  and  yet  increase  the  power 
that  is  transmitted  by  increasing  VM  the  voltage  at  the  motor, 
using  in  fact  a  high-voltage  motor,  and  of  course  a  high- 
voltage  generator  to  correspond.  To  put  the  matter  in 
another  way.  Let  VQ  be  the  volts  at  the  generator  end  of  the 
line,  (VG  —  VM)/R  will  be  =  i.  Now  we  may  keep  i  constant 
(and  therefore  the  i2K,  loss  constant)  and  yet  increase  the  volt- 
ages, provided  VG  —  VM  remains  as  before. 

Example.  —  Suppose  a  line  of  copper-wire  20  miles  long  has 
resistance  of  100  ohms.  A  current  of  6  amperes  in  it  will 
waste  3600  watts  or  nearly  5  horse-power.  To  send  6 
amperes  through  100  ohms  requires  a  difference  of  po- 
tentials of  600  volts.  Suppose  VG  =  1000  and  VM  =  400, 
VG  -  VM  =  600.  The  watts  sent  in  are  iVG  =  6000, 
and  the  watts  delivered  are  iVM  =  2400.  Of  8  horse-power 
put  in  only  about  3j  are  delivered,  the  efficiency  being 
VM/VG  =  40  per  cent.  Now  suppose  VG  increased  to  2000 
volts,  and  VM  •  to  1400.  VG  -  VM  =  600,  as  before. 
i  =  6  amperes,  as  before.  i*R  loss  is  3600  watts,  as  be- 
fore. But  watts  sent  in  are  now  12,000  (over  16  H.P.), 
and  the  watts  delivered  are  8400  (11J  H.P.),  whilst  the 
efficiency  is  now  70  per  cent. 


CH.  xi.  552]          TRANSMISSION   OF   POWER  537 

Another  way  to  state  the  matter  is  that  for  a  given  amount 
of  power,  the  higher  the  voltage,  the  smaller  may  be  the 
current,  and  therefore  the  smaller  the  size  of  the  copper  wires 
required. 

It  is  therefore  clear  that  high  voltage  is  the  secret  of  success 
in  the  electrical  transmission  of  energy,  whether  for  lighting 
or  power,  to  long  distances. 

552.  Long-distance  Transmission.  —  Owing  to  the  ease 
with  which  the  voltage  can  be  raised  or  lowered  by  the  use 
of  stationary  transformers  (Art.  538)  alternating  currents 
are  almost  always  preferred  for  long-distance  transmission : 
and  three-phase  currents  are  preferred  to  single-phase  be- 
cause of  the  greater  economy  of  copper  for  equal  maxima  of 
potential  difference. 

There  are  in  Great  Britain  few  examples  of  long-distance 
transmission  because  of  the  lack  of  large  water-power  stations. 
In  the  transmission  of  energy  from  the  Falls  of  Tivoli  to  light 
the  city  of  Rome  sixteen  miles  away,  a  pressure  of  5000 
volts  is  used.  At  the  great  power  station  of  Niagara  the 
currents  are  distributed  in  the  district  at  2250  volts,  but  for 
transmission  to  Buffalo,  16  miles  distant,  the  voltage  is  raised 
to  11,000.  An  American  transmission  system  conveys  energy 
at  a  pressure  of  150,000  volts  from  Big  Creek  to  Los  Angeles, 
California,  240  miles  away.  This  system  is  three-phase 
and  transmits  120,000  kilowatts. 

The  Thury  System  is  a  series  transmission  scheme  using 
high  voltage  and  a  constant  continuous  current;  for  which 
the  insulation  need  not  be  as  good  as  for  an  alternating  cur- 
rent system  of  the  same  voltage.  In  the  Moutiers-Lyon 
transmission  line  an  area  of  300  square  miles  is  supplied,  the 
transmission  lines  being  supported  overhead.  The  voltage 
in  use  is  58,000  volts  on  a  three- wire  system  (Art.  559),  the 
earth  being  used  as  a  middle  wire.  Motors  and  generators 
are  all  connected  in  series  in  this  system,  and  when  it  is  re- 
quired to  stop  any  machine  the  brushes  are  rocked  round  to 
their  non-acting  position  and  then  the  machine  is  short-cir- 


538         ELECTRICITY   AND   MAGNETISM      [PT.  n.  553,  554 

cuited ;    while  the  reverse  operations  are  used  for  starting 
up. 

553.  High  Voltage  and  Extra-high  Voltage.  —  Supply 
systems  may  be  classified  according  to  whether  they  operate 
at  a  low  voltage  (or  low  pressure),  i.e.  from  100  volts  (or  under) 
to  300  volts ;  high  voltage,  i.e.  from  300  to  3000  volts ;  or 
extra  high  voltage,  over  3000  volts.  High- volt  age  systems 
generally  (but  not  necessarily)  employ  alternating  currents, 
with  transformers  (Art.  538)  to  transform  to  low  pressure 
suitable  for  use  in  the  consumers'  houses. 

Example.  —  The  Charing  Cross  Electric  Supply  Company 
generates,  at  its  power  station  at  Bow,  alternating  cur- 
rents (three-phase)  at  10,000  volts,  which  are  supplied 
to  various  substations  in  London  through  extra-high 
pressure  feeders  placed  underground.  The  substations 
contain  motor-generators  (Art.  544)  and  battery  plant. 
The  motor-generators  convert  the  10,000-volt  alternat- 
ing currents  into  400-volt  continuous  currents,  with  a 
corresponding  increase  of  amperes  delivered.  The  400- 
volt  supply  is  connected  across  the  outer  mains  (Art. 
559)  of  a  three-wire  distributing  system  which  supplies 
the  customers  at  200  volts  for  lighting  or  400  volts  for 
motor  power. 


LESSON  XLIX.  —  The  Distribution  of  Power 

554.  Power  Stations.  —  Electrical  energy  on  a  large  scale 
is  usually  generated  at  Central  Stations  or  Power-houses. 
These  buildings  contain  the  prime  movers  :  —  steam-engines, 
steam-turbines,  water-turbines,  or  gas  engines,  etc.,  and  the 
generating  plant :  —  dynamos  or  alternators.  Steam-power 
stations  are  erected  in  convenient  positions,  where  coal  is 
easily  accessible,  generally  near  a  plentiful  supply  of  water 
for  the  condensing  plant,  etc.,  and  should  not  be  erected  in 
the  middle  of  towns. 

The  generating  plant  of  a  power  station  is  in  several  dis- 
tinct and  complete  sets  (dynamo  and  prime  mover  complete) . 
This  is  more  economical  than  one  large  set  as  the  number  of 


CH.  xi.  555-557]  DISTRIBUTORS  539 

sets  in  use  will  depend  on  the  demand  upon  the  power 
station,  and  so  each  set  can  be  run  at  nearly  full  load,  at 
which  load  most  machines  give  their  best  efficiency. 

Power  stations  also  contain  a  switch-board  for  the  central 
control  of  all  the  machines.  A  separate  panel  is  used  for 
each  machine  so  that  in  the  case  of  a  breakdown  of  one 
machine  it  can  be  immediately  isolated. 

The  Lot's  Road  Power  Station  (Fig.  328)  contains  eight 
6000-kilowatt  turbo-generators,  which  supply  energy  to  most 
of  the  London  underground  electric  railways. 

A  daily  record  of  the  performance  of  each  set  is  made  by 
recording  instruments  mounted  upon  the  switch-board. 

555.  Feeders.  —  The    distribution    of    electrical    energy 
from  the  power-houses  to  the  several  convenient  centres  in 
the  area  supplied  is  accomplished  by  cables  called  feeders. 
The  feeders  are  of  sufficient  cross-sectional  area  to  convey, 
without  undue  heating,  the  maximum  demand  of  current. 
Feeders  generally  connect  the  power-house  to  substations, 
and  are  laid  underground  in  pipes,  or  supported  on  poles  or 
structures  above  ground. 

556.  Substations.  —  The  feeders  generally  convey  current 
at  a  higher  pressure,  for  economic  reasons,  than  is  suitable 
for  conveyance  to  the  consumers'   premises.     Substations 
therefore  contain  electrical  plant  for  the  conversion  of  the 
voltage  into  a  suitable  value.     The  conversion  of  continuous 
current  voltage  requires  rotating  machines  called  motor- 
generators  (Art.  544),  whereas  alternating  currents  do  not; 
stationary  transformers  (Art.  538)  being  used.     To  convert 
continuous  current  into  alternating  current  or  vice  versa, 
rotatory  converters  (Art.  546)  are  used. 

557.  Distributors. — From  the  substations  numerous  cables 
connect  them  to  the  consumers'  premises,  these  are  called 
distributors.      The   distributors  are  composed   of  stranded 
conductors,  either  copper  or  aluminium,  covered  with  some 
insulating  compound  such  as  gutta-percha,  treated  paper,  or 
bitumen,  and  are  laid  mostly  in  conduits  underground. 


540 


ELECTRICITY  AND  MAGNETISM      [PT.  n.  557 


CH.  xi.  557] 


POWER  STATIONS 


541 


542  ELECTRICITY   AND   MAGNETISM     [PT.  n.  558 

558.  Conditions  of  Electric  Supply.  —  Electric  energy  is 
almost  always  supplied  under  one  of  two  standard  conditions, 
either  — 

(a)  at  Constant  Voltage,  or 

(b)  with  Constant  Current. 

In  the  former  case  the  circuit  is  branched,  and  the  current 
is  supplied  (usually  at  100  volts)  to  all  the  lamps  or  motors 
in  parallel  (Fig.  330),  each  lamp,  etc.,  being  '  independent  of 
all  others  ;  and  the  current  varying  precisely  in  proportion 
to  the  demand. 

The  current  in  the  mains  subdivides  and  flows  through 

each      lamp      independently. 

~~T      T    T    T     T      T"    When  any  lamp  is  switched 

T     T    T    r    T     T     °n  it  does  not  diminish  the 

current  in  the  others,  but  by 

FXG.  330.  -Distribution  in  Parallel.  ^    additional    path 


it  simply  causes  more  current  to  flow  from  the  source  of 
supply.  The  method  of  grouping  in  series  (Art.  176)  is 
seldom  used  for  glow-lamps,  since  each  lamp  would  then 
require  an  automatic  cut-out  to  prevent  the  rest  of  the  row 
from  being  extinguished  in  case  one  lamp  went  out. 

In  the  latter  case,  seldom  used  except  for  long  rows  of  arc- 
lamps,  the  circuit  is  undivided,  and  the  current  (usually 
10  amperes)  flows  through  all  the  lamps  in  series.  If  lamps 
are  turned  out  (by  short-circuiting  them)  the  voltage  must 
be  reduced  to  keep  the  current  constant. 

Since  the  power  of  a  current  depends  on  the  voltage  at 
which  it  is  supplied,  the  unit  of  supply  recognized  in  law  is 
based  on  the  unit  of  power,  the  watt  (Art.  454)  .  The  "  unit  " 
is  defined  as  1000  watts  supplied  for  one  hour  (i.e.  1  kilowatt- 
hour)  or  its  equivalent.  The  maximum  price  which  the 
English  Board  of  Trade  permits  the  supply  company  to 
charge  the  consumer  for  1  "  unit  "  is  eightpence.  In  Lon- 
don the  average  price  charged  by  the  supply  authorities  is 
about  2-15  pence  per  "  unit." 


CH.  xi.  559,  560] 


EFFECT   OF   LOADS 


543 


-5 


IMJUL 
1 


FIG.  331.  —  Distribution  by  Three-wire 
System. 


559.  Three-wire  System.  —  Three-wire  systems,  in  which 
a  third  or  neutral  wire  is  introduced  between  the  -f  and  the 
—  main,  have  been  devised  to 

enable  higher  voltages  to  be 
used,  and  thereby  enable 
twice  as  many  lamps  to  be 
lit  with  little  additional  ex- 
penditure in  copper.  To  ren- 
der the  lamps  on  one  side  of 
the  circuit  (Fig.  331)  inde- 
pendent of  those  on  the  other,  in  case  an  equal  number  do 
not  happen  to  be  switched  on  at  the  same  time,  the  middle 
wire  (which  only  need  be  thick  enough  to  carry  a  current 
equal  to  the  difference  between  the  currents  in  the  two  outer 
wires)  is  carried  back  to  the  station  and  kept  at  mean  poten- 
tial between  the  two  outer  wires  by  the  used  of  two  dynamos 
instead  of  one. 

560.  Effect  of  Various  Loads.  —  The  load  on  an  average 
power  station  may  be  divided  iiito  three  chief  parts;    (i.) 

for  motors,  (ii.)  lighting,  (iii.) 
heating  and  miscellaneous  re- 
quirements. The  motor  load  be- 
gins about  7  A.M.,  when  various 
works  commence  (see  Fig.  332), 
and  lasts  throughout  the  day 
until  about  8  P.M.,  but  before  the 
works  leave  off  there  is  a  demand 
for  power  for  lighting  which 
causes  a  peak  load  about  7  P.M. 
The  time  of  the  peak  load  varies 
12  2  *  e  s  ioj2  2  4  e  a  1012  with  the  season  and  weather  con- 

morning        noon    Afternoon  Night 
FIG.  332.  —  A  Daily  Load-curve.       ditions.         Occasionally,      due      to 

storms,    abnormal    demands    of 

power  are  made  for  lighting  in  the  daytime  and  this  with  the 
motor  and  heating  load  is  generally  more  than  the  normal 
full  output  of  the  station-machinery.  For  these  periods  a 


5000 


544  ELECTRICITY  AND   MAGNETISM     [PT.  n.  561 

battery  of  accumulators  (Art.  572)  is  usually  employed  to 
assist  the  generating  plant  in  a  storm  load. 

The  load  on  a  generating  set  continually  alters,  and  this 
causes  a  corresponding  variation  in  the  voltage,  and  as  the 
variation  must  not  exceed  a  certain  amount  it  is  necessary 
periodically  to  adjust  the  voltage.  The  adjustment  can 
either  be  made  by  hand  regulation  which  operates  a  resist- 
ance or  by  an  automatic  device  such  as  the  Tirrill  regulator. 

561.  Protective  Devices.  —  Many  devices  have  been  em- 
ployed to  protect  overhead  transmission  lines,  telegraph  and 
telephone  lines,  from  the  disastrous  effects  resulting  from 
being  struck  by  lightning.  The  oldest  of  these  consist  of 
serrated  plates  placed  nearly  in  contact,  Fig.  333  a,  providing 
an  easy  passage  to  earth  for  any  sudden  discharge  that  is 
able  to  jump  the  gap  between  the  plates.  To  prevent  arcs 
following  the  spark,  in  electric  light  or  power  lines,  a  number 
of  zinc  cylinders  lying  close  to  one  another,  forming  a  multiple 
spark-gap,  Fig.  333  6,  are  sometimes  used.  Another  device 
is  to  give  to  the  discharge  surfaces  the  form  of  a  pair  of 
curved  horns,  as  in  Fig.  333  c,  so  that  any  arc,  following  the 
discharge,  in  ascending  the  horns  extends  itself  and  goes 
out.  This  is  sometimes  combined  with  a  copper  wire  coil, 
which  acts  as  an  impedance  in  the  line,  and  at  the  same  time 
helps  to  blow  out  the  discharge  magnetically.  A  fourth  de- 
vice, Fig.  333  d,  consists  of  introducing  a  resistance  rod  of 
carborundum  in  series  with  a  number  of  insulated  metallic 
surfaces  which  act  as  a  multiple  spark-gap  to  quench  the 
spark.  Electrolytic  arresters  are  also  used.  These  consist 
of  a  number  of  cone-shaped  trays  of  aluminium,  on  which 
is  coated  a  film  of  aluminium  hydroxide.  These  trays  are 
placed  together  one  in  the  other,  but  kept  apart  by  insulating 
spacers  and  each  tray  filled  with  a  suitable  electrolyte.  The 
resistance  of  the  film  of  each  tray  is  sufficient  to  prevent  the 
breakdown  of  it  by  voltages  below  300.  The  number  of  trays 
to  be  used  will  therefore  depend  on  the  voltage  of  the  system. 

It  is  also  necessary  to  protect  machines  and  circuits  from 


CH.  xi.  561] 


PROTECTIVE    DEVICES 


545 


accidental  short-circuit.  For  this  purpose  either  fuses  or 
circuit-breakers  are  employed.  Fuses  (Art.  464)  consist  of 
specially  isolated  pieces  of  metal  through  which  the  current 
passes,  so  that  if  the  current  exceed  a  certain  value,  depend- 


LINE 


LINE 


a 


vwwwwv 

AAAAAAAA/VS. 


d 


~ 

FIG.  333  c.  FIG.  333  d. 

Various  Forms  of  Lightning  Arresters. 

ing  on  the  size  and  material  of  the  fuse,  it  melts,  thus  break- 
ing the  circuit.  Circuit-breakers  are  automatic  contact 
devices  iri  which  the  excessive  current  is  made  to  act  electro- 
magnetically  on  a  trip-gear  and  open  the  circuit.  The  trip 
works  against  a  spring  and  thus,  by  adjustments  to  the 
strength  of  the  spring,  the  breaker  can  be  set  to  open  the 
circuit  at  any  prearranged  limit  of  current.  Circuit-breakers 
which  have  to  operate  with  heavy  currents  are  generally  pro- 
vided with  auxiliary  contacts  of  carbon  so  that  the  final 
break  of  the  current  occurs  when  the  copper  contacts  have 
already  parted.  The  arc  which  forms  between  the  carbon 
contacts  is  blown  out  by  an  electromagnetic  device  similar 
to  Fig.  333  c  above  and  thus  no  damage  is  done  by  the  arc 
fusing  the  contacts. 

2N 


CHAPTER  XII 

ELECTRIC   TRACTION 

LESSON  L.  —  Electric  Tramways  and  Railways 

562.  Electric  Locomotion.  —  After  the  invention  of  elec- 
tric motors  many  suggestions  were  made  to  propel  vehicles 
by  electricity,  as  by  Davenport  (1835),  Davidson  (1838), 
and  Roloff  (1868),  but  the  great  cost  and  trouble  of  primary 
batteries  (Art.  176)  prevented  any  success.  Only  when  the 
dynamo  was  commercially  introduced  for  generating  electric 
current  did  electric  locomotion  become  possible.  The  first 
practical  suggestions  for  the  electric  propulsion  of  tram-cars 
came  independently  from  Werner  Siemens,  Stephen  Field, 
and  T.  A.  Edison,  in  1879.  In  1883  the  Portrush  Railway 
in  Ireland,  in  which  current  was  supplied  to  the  cars  by 
means  of  a  third  rail,  was  opened  for  traffic.  In  1888  Daft 
introduced  the  method  of  taking  current  from  an  overhead 
line  by  an  underrunning  trolley-wheel  on  the  end  of  an  ele- 
vated pole;  and  in  1890  Siemens  and  Halske  devised  the 
underrunning  contact-bow  for  the  same  purpose.  The  great 
development  of  tramways  with  overhead  conductors  took 
place  in  the  United  States,  beginning  in  the  years  1888  to 
1890.  In  1890  also  the  first  subterranean  tube-railway, 
using  third  rail,  the  City  &  South  London  Railway,  was 
opened.  The  extensive  systems  of  tube-railways  in  London 
and  Paris  followed.  There  are  now  85  miles  of  underground 
railways  in  London  alone.  The  application  of  electric  pro- 
pulsion to  railway  lines  of  full  gauge  and  with  heavy  rolling 
stock,  with  the  use  of  alternating  currents,  was  largely  de- 
veloped in  Switzerland  and  North  Italy  from  1899  onwards ; 
and  in  the  United  States,  using  continuous  currents,  at  about 

546 


CH.  xii.  563]  ELECTRIC   TRAMWAYS  547 

the  same  epoch.  The  three  main  branches  of  the  subject  are 
the  applications  to  (i.)  Tramways,  (ii.)  Railways,  (iii.)  Auto- 
mobiles. 

563.  Tramways.  —  There  are  several  ways  of  conveying 
the  electric  current  to  the  moving  car :  — 

(a)  Current  (usually  continuous  current  at  500  volts)  is 
supplied  from  the  power-house  or  from  a  substation  to  an 
overhead  line,  with  which  the  car  makes  contact  as  it  runs 
by  means  of  a  trolley-wheel  (or  a  metal  bow)  fixed  on  a 
jointed  pole  above  the  car.  The  current  passes  down  an 
insulated  lead  from  the  trolley-wheel,  through  the  controller 
and  the  motors,  to  the  car  wheels  and  so  to  the  rails,  which 
serve  as  the  return  conductor;  the  rails  being  bonded 
together  by  copper  bonds  to  ensure  good  conductance.  In 
many  cases  there  are  also  return  feeders  from  the  rails  to  the 
power-house  (or  substation). 

(6)  Current  is  picked  up  by  the  car  from  conductors  laid 
in  a  slot-conduit  in  the  road  between  the  rails,  by  means  of 
a  contact-piece,  or  "  plough  "  let  down  into  the  slot. 

(c)  Current  is  picked  up  by  the  car  from  metal  studs 
slightly  projecting  from  the  road-surface  between  the  rails, 
by  means  of  a  long  skate  fastened  under  the  car ;  each  stud 
being  automatically  connected  to  the  underground  mains 
as  the  car  comes  up,  and  disconnected  as  it  passes  on.  This 
plan,  though  cheaper  than  (fr),  has  dropped  into  disuse 
through  practical  difficulties. 

For  tram-car  driving,  two  series- wound  motors  (Art.  521) 
are  mounted  on  the  truck  of  each  car,  and  drive  the  wheels 
through  a  single-reduction  gear.  The  amount  of  current 
taken  from  the  line  is  regulated  by  moving  the  handle  of  a 
controller,  a  complicated  kind  of  barrel  switch,  performing 
the  following  operations:  (i.)  at  starting,  the  controller 
switches  on  the  current  to  the  two  motors  in  series,  with 
additional  resistance  in  circuit,  so  that  each  motor  at  start- 
ing gets  less  than  half  the  voltage ;  (ii.)  as  speed  increases, 
the  controller  cuts  out  the  added  resistance,  in  stages ;  (iii.) 


548  ELECTRICITY  AND   MAGNETISM      [PT.  n.  564 

then  puts  the  two  motors  in  parallel,  with  resistance ;  (iv.) 
cuts  out  the  resistance,  in  stages;  (v.)  at  highest  speed 
shunts  part  of  the  current  from  the  magnet-windings  so  as 
to  weaken  the  magnets  (Art.  521).  The  controller  also  con- 
tains devices  for  reversing  the  direction  of  the  rotation  of 
the  motors.  Each  motor  is  usually  of  25  to  30  H.P.,  and  has 
four  poles.  The  power  required  by  the  car  running  on  the 
level  is  from  10  to  25  kilowatts ;  the  current  at  starting 
being  some  100  amperes  (to  give  the  initial  starting  effort), 
and  from  2  to  5  amperes  when  running  fast. 

564.  Railways.  —  For  suburban  traffic,  where  there  is 
frequent  starting  and  stopping,  and  rapid  acceleration  is 
essential,  the  motors  must  exert  great  initial  torque.  If 
separate  electric  locomotives  are  employed  to  draw  a  train 
of  six,  eight,  or  ten  cars  they  must  be  from  600  H.P.  to  1000 
H.P.  But  in  most  cases  motor-coaches  are  provided  having 
the  motors  under  the  floors  of  the  cars,  each  motor-coach 
being  able  to  propel  itself  and  one  or  two  trailer  cars,  the 
trains  being  made  up  of  such  units.  In  the  Liverpool  and 
Southport  section  of  the  Lancashire  &  Yorkshire  Railway, 
motor-coaches  are  used  having  four  motors  of  150  H.P.  each, 
each  train  consisting  of  4  coaches  in  total.  In  most  English 
suburban  lines  the  current  is  picked  up  from  a  third  rail. 
At  the  usual  pressure  of  500  to  600  volts  (continuous  current) 
the  current  needed  by  a  100  H.P.  motor  is  from  200  to  250 
amperes  during  the  period  of  acceleration;  but  when  a 
speed  of  20  miles  per  hour  has  been  reached,  the  current  is 
greatly  reduced.  An  electrically  propelled  train  may  attain 
this  speed  in  the  short  period  of  10  seconds.  For  long  lines, 
where  the  traffic  is  carried  on  with  ordinary  cars  or  waggons, 
locomotives  are  a  necessity.  If  the  supply  is  at  600  to  750 
volts,  then  for  a  locomotive  actually  working  at  1000  H.P., 
the  amount  of  current  taken  will  be  not  far  from  1000 
amperes ;  and  at  starting  the  amount  taken  may  be  double 
this  to  give  the  required  effort.  In  order  to  diminish  the 
cost  of  the  feeding  mains,  for  long  lines,  the  current  (usually 


CH.  xii.  564]  ELECTRIC   RAILWAYS 


549 


550  ELECTRICITY  AND  MAGNETISM      [PT.  n.  565 

alternating)  is  supplied  at  extra-high  pressures,  such  as  6000 
volts,  to  sub-stations  where  converters  (Art.  546)  are  in- 
stalled. In  certain  Swiss  and  Italian  railroads  three-phase 
currents  (Art.  535)  are  employed  throughout;  whilst  in 
other  instances  single-phase  motors  are  preferred.  In  these 
high-pressure  three-phase  and  single-phase  lines  overhead 
conductors  are  used.  A  modern  electric  locomotive  of  2000 
H.P.  weighs  from  80  to  100  tons,  and  is  about  40  feet  long; 
while  a  modern  steam  locomotive  of  1500  H.P.  weighs,  with 
its  tender,  about  150  tons  and  is  about  60  feet  long ;  further, 
the  running  cost  of  the  electric  locomotive  per  train-mile  is 
distinctly  lower  than  that  of  the  steam  locomotive.  The 
electric  locomotive  (Fig.  334),  as  used  on  the  Metropolitan 
Railway,  London,  weighs  46  tons,  and  has  four  motors  of 
250  H.P.  each. 

565.  Electric  Automobiles.  —  An  automobile  must  neces- 
sarily carry  a  battery  to  drive  the  electric  motors,  and  this 
battery  must  consist  of  accumulators  that  are  systematically 
recharged.  Lead  cells  (Art.  572)  are  heavy,  and  deteriorate 
under  mechanical  shocks.  Edison's  nickel-oxide  accumula- 
tor (Art.  573)  was  designed  expressly  to  be  lighter  and  to 
withstand  jars.  For  propelling  delivery-cars,  cabs,  and  light 
vehicles  electric  automobiles  have  great  usefulness.  For  a 
daily  run  of  25  to  40-  miles  about  town  the  energy  consump- 
tion is  about  0-48  kilowatt-hour  (or  "  unit  ")  per  mile  per 
ton.  For  a  total  weight  (vehicle  and  load)  of  5  tons  it  is 
usual  to  provide  a  battery  of  60  cells  of  accumulators,  having 
a  charge-limit  of  27,000  ampere-hours.  It  is  usual  to  fit  the 
vehicle  with  a  series-wound  motor. 


CHAPTER  XIII 

ELECTRO-CHEMISTRY 

LESSON  LI.  —  Electrolysis 

666.  Electromotive-force  of  Polarization.  —  The  simple 
laws  of  definite  chemical  action  due  to  the  current  having 
been  laid  down  in  Lesson  XIX.,  it  remains  to  consider  the 
relations  between  the  chemical  energy  and  its  electrical 
equivalent.  Whenever  an  electrolyte  is  decomposed  by  a 
current,  the  resolved  ions  have  a  tendency  to  reunite,  that 
tendency  being  commonly  termed  "  chemical  affinity." 
Thus  when  zinc  sulphate  (ZnSO^  is  split  up  into  Zn  and  SCU 
the  zinc  tends  to  dissolve  again  into  the  solution,  and  so 
spend  the  potential  energy  of  the  system.  But  zinc  dissolv- 
ing into  sulphuric  acid  sets  up  an  electromotive-force  of 
definite  amount;  and  to  tear  the  zinc  away  from  the  sul- 
phuric acid  requires  an  electromotive-force  at  least  as  great 
as  this,  and  in  an  opposite  direction  to  it.  So,  again,  when 
acidulated  water  is  decomposed  in  a  voltameter,  the  sepa- 
rated hydrogen  and  oxygen  tend  to  reunite  and  set  up  an 
opposing  electromotive-force  of  no  less  than  149  volts. 
This  opposing  electromotive-force,  which  is  in  fact  the 
measure  of  their  "  chemical  affinity  "  is  termed  the  electro- 
motive-force of  polarization.  It  can  be  observed  in  any 
water  voltameter  (Art.  259)  by  simply  disconnecting  the 
wires  from  the  battery  and  joining  them  to  a  galvanometer, 
when  a  current  will  be  observed  flowing  back  through  the 
voltameter  from  the  hydrogen  electrode  towards  the  oxygen 
electrode.  The  polarization  in  a  voltaic  cell  (Art.  183)  pro- 
duces an  opposing  electromotive-force  in  a  perfectly  similar 
way. 

551 


552  ELECTRICITY  AND   MAGNETISM     [PT.  n.  567 

Now,  since  the  affinity  of  hydrogen  for  oxygen  is  repre- 
sented by  an  electromotive-force  of  149  volts,  it  is  clear 
that  no  cell  or  battery  can  decompose  water  at  ordinary 
temperatures  unless  it  has  an  electromotive-force  of  at  least 
149  volts.  With  every  electrolyte  there  is  a  similar  mini- 
mum electromotive-force  necessary  to  produce  complete 
continuous  decomposition. 

567.  Electrochemical  Energy.  —  Suppose  a  current  to 
convey  a  quantity  of  electricity  Q  through  a  circuit  in  which 
there  is  an  opposing  electromotive-force  E :  the  work  W 
done  in  moving  Q  units  of  electricity  against  this  electro- 
motive-force will  be  equal  to  E  X  Q.  If  E  and  Q  are  ex- 
pressed in  "  absolute  "  C.G.S.  units,  E  X  Q  will  be  in  ergs. 
If  E  is  in  volts  and  Q  is  in  coulombs,  the  product  will  be  the 
work  in  joules.  The  total  energy  of  the  current,  as  available 
for  producing  heat  or  mechanical  motion,  will  be  diminished 
by  this  quantity,  which  represents  the  work  done  against 
the  electromotive-force  in  question. 

But  we  can  arrive  in  another  way  at  an  expression  for  this 
same  quantity  of  work.  The  quantity  of  electricity  in  pass- 
ing through  the  cell  will  deposit  a  certain  amount  of  metal : 
this  amount  of  metal  could  be  burned,  or  dissolved  again  in 
acid,  giving  up  its  potential  energy  as  heat,  and,  the  mechani- 
cal equivalent  of  heat  being  known,  the  equivalent  quantity  of 
work  can  be  calculated.  Q  units  of  electricity  will  cause  the 
deposition  of  Qz  grammes  of  an  ion  whose  absolute  electro- 
chemical equivalent  is  z.  [For  example,  z  for  hydrogen  is 
0-0001044  gramme,  being  ten  times  the  amount  (see  Table  in 
Art.  256)  deposited  by  one  coulomb,  for  the  coulomb  is  TV  of 
the  absolute  C.G.S.  unit  of  quantity.]  If  H  represents  the 
number  of  heat  units  evolved  by  one  gramme  of  the  substance, 
when  it  enters  into  the  combination  in  question,  then  QzH 
represents  the  value  (in  heat  units)  of  the  chemical  work  done 
by  the  flow  of  the  Q  units ;  and  this  value  can  immediately 
be  translated  into  ergs  of  work  by  multiplying  by  Joule's 
equivalent  J  (=  42  X  106).  [See  Table  on  page  224.] 


CH.  xni.  567]     ELECTROCHEMICAL  ENERGY  553 

» 
We  have  therefore  the  following  equality : 

EQ  =  QzHJ  ;  whence  it  follows  that 

E  =  zHJ ;  or,  in  words,  the  electromotive-force 
of  any  chemical  reaction  is  equal  to  the  product  of  the  electro- 
chemical equivalent  of  the  separated  ion  into  its  heat  of  com- 
bination, expressed  in  dynamical  units. 

Examples.1  —  (1)  Electromotive-force  of  Hydrogen  tending  to 
unite  with  Oxygen.  For  Hydrogen  z  =  0*0001044 ;  H 
(heat  of  combination  of  one  gramme)  =  34000  gramme- 
degree-units  ;  J  =  42  X  106. 

0-0001044  X  34000  X  42  X  106  =  T49  X  108    "  absolute  " 
units  of  electromotive-force,  or    =  1*49  volts. 

(2)  Electromotive-force  of  Zinc  dissolving  into  Sulphuric  Acid. 
z  =  0-00339 ;    H  =  1670  (according  to  Julius  Thomsen) ; 
J  =  42  X  106. 

0-00339  X  1670  X  42  X  106  =  2'377  X  108. 
or    =  2-377  volts. 

(3)  Electromotive-force    of    Copper    dissolving    into    Sulphuric 
Acid,     z  =  0-00329 ;    H  =  909'5 ;    J  =  42  X  106. 

0-00329  X  909-5  X  42  X  10  =  1-256  X  108, 
or    =  1-256  volts. 

(4)  Electromotive-force  of  a  Daniell's  Cell.     Here  zinc  is  dis- 
solved at  one  pole  to  form  zinc  sulphate,  the  chemical 
action  setting  up  a  +  electromotive-force,  while  at  the 
other  pole  copper  is  deposited  by  the  current  out  of  a 
solution  of  copper  sulphate,  thereby  setting  up  an  oppos- 
ing   (or   — )    electromotive-force.     That    due    to    zinc    is 
shown  above  to  be  +  2 '377  volts,  that  to  deposited  copper 
to  be   —   1"256.      Hence    the  nett  electromotive-force  of 
the    cell    is    (neglecting     the     slight     electromotive-force 
where  the  two    solutions    touch)  2'377  -   1-256    =   1-121 
volts.     This  is  nearly  what  is  found  (Art.  196)  in  practice 
to  be  the  case.     It  is  less  than  will  suffice  to  electrolyze 
water,    though   two    Daniell's   cells   in   series   electrolyze 
water  easily. 

1  The  figures  given  in  these  examples  as  well  as  those  on  p.  555  for  the 
heat  of  combination  must  be  taken  as  only  approximate.  The  heat  of 
combination  is  different  at  different  temperatures,  and  the  heat  evolved  by 
the  salt  dissolving  in  water  must  also  be  taken  into  account.  In  fact  von 
Helmholtz  showed  that  the  expression  zHJ  is  incomplete,  and  that  to  it 
should  be  added  a  term  6  '  dE/d9,  wherein  Q  is  the  absolute  temperature  of 
the  cell. 


554  ELECTRICITY  AND   MAGNETISM     [PT.  n.  568 

Since  1  horse-power-hour  =  746  watt-hours  =  746  ampere- 
hours  at  1  volt,  it  follows  that  at  V  volts  the  number  of 
ampere-hours  will  =  746  -j-  V.  Now  as  the  weight  of  zinc 
consumed  in  a  cell  is  1-219  grammes  per  ampere-hour  (when 
there  is  no  waste),  and  as  1  Ib.  equals  453-6  grammes,  the 
consumption  will  be  as  follows : 

Weight  of  zinc  used    1      746        2  =  2  ^ 

per  horse-power-hour  J        V  '  V 

Hence  the  quantity  of  zinc  that  must  be  consumed  to  gener- 
ate 1  horse-power-hour  in  any  battery  of  cells  cannot  be  less 
than  2  Ibs.  -f-  the  available  volts  of  a  single  cell  of  the  battery ; 
and  zinc  costs  about  8  pence  per  pound. 

Example.  —  If  a  new  cell  can  be  invented  to  give  2  volts  at  its 
terminals  when  in  full  work,  a  battery  of  such  cells,  how- 
ever arranged,  will  consume  1  Ib.  of  zinc  per  hour  per 
horse-power,  or  T34  Ibs.  per  "  unit  "  (or  kilowatt-hour)  of 
supply. 

An  equivalent  quantity  of  exciting  and  depolarizing  chemi- 
cals will  also  be  used,  and  these  will  increase  the  total  cost 
per  unit.  It  is  clear  that  as  a  source  of  public  supply  pri- 
mary batteries  consuming  zinc  can  never  compete  in  price 
with  dynamos  driven  by  steam.  The  actual  cost  of  coal  to 
central  stations  in  London  is  about  0-3  pence  per  "  unit "; 
and  the  maximum  legal  price  that  a  supply  company  may 
charge  in  Great  Britain  for  electric  energy  is  eightpence  per 
"  unit."  See  Art.  558. 

568.  Electrochemical  Power  of  Metals.  —  The  accom- 
panying Table  gives  the  electromotive-force  of  the  different 
metals  as  calculated  (Art.  567)  from  the  heat  evolved  by  the 
combination  with  oxygen  of  a  portion  of  the  metal,  equiva- 
lent electrochemically  in  amount  to  one  gramme  of  hydrogen. 
The  figures  in  the  second  column  are  in  calories.  The  figures 
in  the  third  column  are  calculated  from  those  in  the  second 
by  multiplying  .by  the  electrochemical  equivalent  of  hydro- 
gen, and  by  Joule's  equivalent  (42  X  106)  and  dividing  by 


CH.  xin.  569]     ELECTROCHEMICAL   RELATIONS 


555 


108,  to  reduce  to  volts.     The  electromotive-forces  as  observed 
(in  dilute  sulphuric  acid)  are  added  for  comparison. 


SUBSTANCE 

HEAT  OF 
OXIDATION 

OP 

EQUIVALENT 

E.M.F.  CALCULATED 

E.M.F. 
OBSERVED 

Relatively 
to  Oxygen 

Relatively 
to  Zinc 

Potassium      .... 
Sodium      

69,800 
67,800 
42,700 
34,120 
34,000 
25,100 
18,760 
9,000 
7,500 
2,000 
0 
-    6,000 

-    6,500 
-  12,150 
-  14,800 
-  25,070 

3'01 
2-91 
1-83 
1-55 
1-47 
1*12 
0'80 
0'39 
0'33 
0*09 
0 
-0'26 

-0'29 
-0'52 
-0-63 
-  1'09 

+  1-18 
+  1'09 
0 
-0-28 
-0-36 
-071 
-    '03 
—    '44 
-    '50 
-    74 
-    '83 
-2-09 

-2-12 
-2'35 
-2-46 
-2'92 

+  1-13 
0 

-0'54 
-  1'047 

-  1'53 

-  1-85 
-  1'94 

-2-23 
-2*52 
-2'64 
-3-03 

Zinc       
Iron 

Hydrogen  

Lead     
Copper 

Silver    

Platinum  
Carbon      
Oxygen      

(Nitric  Acid)       .     .     . 
(Black  Oxide  of  Man- 
ganese) .... 

(Peroxide  of  Lead) 
(Ozone) 

(Permanganic  Acid)     . 

The  order  in  which  these  metals  are  arranged  is  in  fact 
nothing  else  than  the  order  of  oxidizability  of  the  metals 
(in  the  presence  of  dilute  sulphuric  acid) ;  for  that  metal 
tends  most  to  oxidize  which  can,  by  oxidizing,  give  out  the 
most  energy.  It  also  shows  the  order  in  which  the  metals 
stand  in  their  power  to  replace  one  another  (in  a  solution 
containing  sulphuric  acid).  In  this  order,  too,  the  lowest 
on  the  list  first,  are  the  metals  deposited  by  an  electric  cur- 
rent from  solutions  containing  two  or  more  of  them :  for 
that  metal  comes  down  first  which  requires  the  least  expen- 
diture of  energy  to  separate  it  from  the  elements  with  which 
it  was  combined. 

569.  General  Laws  of  Electrolytic  Action.  —  In  addition 
to  Faraday's  quantitative  laws  givert  in  Art.  256,  the  follow- 
ing are  important : 


556  ELECTRICITY   AND   MAGNETISM     [PT.  n.  569 

(a)  Every  electrolyte  is  decomposed  into  two  portions, 
an  anion  and  a  kation,  which  may  be  themselves  either 
simple  or  compound.  In  the  case  of  simple  binary  com- 
pounds, such  as  fused  salt  (NaCl),  the  ions  are  simple  ele- 
ments. In  other  cases  the  products  are  often  complicated 
by  secondary  actions.  It  is  even  possible  to  deposit  an 
alloy  of  two  metals  —  brass  for  example  —  from  a  mixture 
of  the  cyanides  of  zinc  and  of  copper. 

(6)  In  binary  compounds  and  most  metallic  solutions,  the 
metal  is  deposited  by  the  current  where  it  leaves  the  cell,  at 
the  kathode. 

(c)  Aqueous  solutions  of  salts  of  the  metals  of  the  alkalies 
and  alkaline  earths  deposit  no  metal,  but  evolve  hydrogen 
owing  to  secondary  action  of  the  metal  upon  the  water. 
From  strong  solutions   of  caustic  potash   and  soda  Davy 
succeeded  in  obtaining  metallic  sodium  and  potassium,  which 
were  before  unknown.     If  electrodes  of  mercury  are  em- 
ployed,  an  amalgam  of  either  of  these  metals  is  readily 
obtained  at  the  kathode.     The  so-called  awwomwra-amal- 
gam  is  obtained  by  electrolysing  a  warm,  strong  solution  of 
salammoniac  between  mercury  electrodes. 

(d)  Metals  can  be  arranged  in  a  definite  series  according 
to  their  electrolytic  behaviour ;  each  metal  on  the  list  behav- 
ing as  a  kation  (or  being  "  electropositive  ")  when  electrolysed 
from  its  compound,  in  preference  to  one  lower  down  on  the  list. 
In  such  a  series  the  oxidizable  metals,  potassium,  sodium, 
zinc,  etc.,  comeJast ;  the  less  oxidizable  or  "  electronegative  " 
metals  preceding  them.     The  order  varies  with  the  nature, 
strength,  and  temperature  of  the  solution  used. 

(e)  From  a  solution  of  mixed  metallic  salts  the  least  elec- 
tropositive metal  is  not  deposited  first,  if  the  current  is  so 
strong  relatively  to  the  size  of  the  kathode  as  to  impoverish 
the   solution   in   its   neighbourhood.     To   deposit   alloys   a 
solution  must  be  found  in  which  both  metals  tend  to  dis- 
solve with  equal  electromotive-forces. 

(f)  The  liberated  ions  appear  only  at  the  electrodes. 


CH.  xiii.  569]          ELECTROLYTIC   ACTIONS  557 

(g)  For  each  electrolyte  a  minimum  electromotive-force  is 
requisite,  without  which  complete  electrolysis  cannot  be 
effected.  (See  Art.  570.) 

(h)  If  the  current  be  of  less  electromotive-force  than  the 
requisite  minimum,  electrolysis  may  begin,  and  a  feeble 
current  may  flow  at  first,  but  no  ions  will  be  liberated,  the 
current  being  completely  stopped  as  soon  as  the  opposing 
electromotive-force  of  polarization  has  risen  to  equality  with 
that  of  the  electrolysing  current. 

(i)  There  is  no  opposing  electromotive-force  of  polariza- 
tion when  electrolysis  is  effected  from  a  dissolving  anode  of 
the  same  metal  that  is  being  deposited  at  the  kathode. 
The  feeblest  cell  will  suffice  to  deposit  copper  from  sulphate 
of  copper  if  the  anode  be  a  copper  plate. 

(j)  Where  the  ions  are  gases,  pressure  affects  the  condi- 
tions but  slightly.  Under  300  atmospheres  acidulated 
water  is  still  electrolysed;  but  in  certain  cases  a  layer  of 
acid  so  dense  as  not  to  conduct  collects  at  the  anode  and 
stops  the  current. 

(k)  The  chemical  work  done  by  a  current  in  an  electrolytic 
cell  is  proportional  to  the  minimum  electromotive-force  of 
polarization. 

(I)  Although  the  electromotive-force  of  polarization  may 
exceed  this  minimum,  the  work  done  by  the  current  in  over- 
coming this  surplus  electromotive-force  will  not  appear  as 
chemical  work,  for  no  more  of  the  ion  will  be  liberated ;  but 
it  will  appear  as  an  additional  quantity  of  heat  (or  "  local 
heat  ")  developed  in  the  electrolytic  cell. 

(ra)  Experiments  show  that  the  resistance  of  a  given 
column  of  a  given  electrolyte  is  a  constant,  no  matter  whether 
larger  or  smaller  currents  are  used  in  testing  the  resistance. 

(n)  Amongst  the  secondary  actions  which  may  occur  the 
following  are  the  chief :  — 

(1)  The  ions  may  themselves  decompose;  as  S04  into  SO3  +  O. 
(2)  The  ions  may  react  on  the  electrodes ;  as  when  acidulated 
water  is  electrolysed  between  zinc  electrodes,  no  oxygen  being 


558  ELECTRICITY  AND   MAGNETISM     [PT.  n.  570 

liberated,  owing  to  the  affinity  of  zinc  for  oxygen.  (3)  The  ions 
may  be  liberated  in  an  abnormal  state.  Thus  oxygen  is  frequently 
liberated  in  its  allotropic  form  as  ozone,  particularly  when  per- 
manganates are  electrolysed.  The  "  nascent "  hydrogen  liber- 
ated by  the  electrolysis  of  dilute  acid  has  peculiarly  active  chemi- 
cal properties.  So  also  the  metals  are  sometimes  deposited  ab- 
normally :  copper  in  a  black  pulverulent  film ;  antimony  (from 
the  terchloride  solution)  in  roundish  gray  masses  which  possess 
a  curious  explosive  property.  When  a  solution  of  lead  is  electro- 
lysed a  film  of  peroxide  of  lead  forms  upon  the  anode.  If  this  be 
a  plate  of  polished  metal  placed  horizontally  in  the  liquid  beneath 
a  platinum  point  as  a  kathode,  the  deposit  takes  place  in  symmet- 
rical rings  of  varying  thickness,  the  thickest  deposit  being  at  the 
centre.  These  rings,  known  as  Nobili's  rings,  exhibit  all  the  tints 
of  the  rainbow,  owing  to  interference  of  the  waves  of  light  occur- 
ring in  the  film.  The  colours  form,  in  fact,  in  reversed  order,  the 
"  colours  of  thin  plates  "  of  Newton's  rings.  (4)  In  certain  cases 
the  deposit  may  be  of  a  non-conducting  nature;  as  for  example, 
where  aluminium  is  the  anode  in  an  alkaline  solution,  and  an  oxide 
of  aluminium  is  formed  as  a  film  which  entirely  stops  the  current. 
Hence  if  a  cell  is  arranged  with  a  small  plate  of  aluminium  and  a 
large  plate  of  lead,  dipping  into  a  solution  of  carbonate  of  soda  or  of 
ammonium  phosphate,  a  current  can  flow  through  it  from  lead  to 
aluminium,  but  not  from  aluminium  to  lead.  Such  a  cell,  called 
Nodon's  valve,  conducts  in  one  direction  only,  and  can  be  used  to 
rectify  an  alternating  current. 

570.  Hypotheses  of  Grotthuss  and  of  Clausius.  —  A 
complete  theory  of  electrolysis  must  explain — first,  the 
transfer  of  electricity,  and  secondly,  the  transfer  of  matter, 
through  the  liquid  of  the  cell.  The  latter  point  is  the  one 
to  which  most  attention  has  been  given,  since  the  "  migra- 
tion of  the  ions  "  (i.e.  their  transfer  through  the  liquid)  in 
two  opposite  directions,  and  their  appearance,  in  free  con- 
dition, at  the  electrodes  only,  are  salient  facts. 

The  hypothesis  put  forward  in  1805  by  Grotthuss  serves 
fairly,  when  stated  in  accordance  with  modern  terms,  to 
explain  these  facts.  Grotthuss  supposes  that,  when  two 
metal  plates  at  different  potentials  are  placed  in  a  cell,  the 
first  effect  produced  in  the  liquid  is  that  the  molecules  of  the 
liquid  arrange  themselves  in  innumerable  chains,  in  which 


CH.  xiii.  570]     HYPOTHESES   OF   ELECTROLYSIS 


559 


every  molecule  has  its  constituent  atoms  pointing  in  a  cer- 
tain direction;  the  atom  of  electropositive  substance  being 
attracted  toward  the  kathode,  and  the  fellow  atom  of  elec- 
tronegative substance  being  attracted  toward  the  anode. 
(This  assumes  that  the  constituent  atoms  grouped  in  the 
molecule  retain  their  individual  electric  properties.)  The 
diagram  of  Fig.  335  shows,  in  the  case  of  hydrochloric  acid, 
a  first  row  of  molecules  distributed  at  random,  and  secondly 


FIG.  335.  —  Grotthuss's  Hypothesis  of  Electrolytic  Action. 

grouped  in  a  chain  as  described.  The  action  which  Grotthuss 
then  supposes  to  take  place  is  that  an  interchange  of  partners 
goes  on  between  the  separate  atoms  all  along  the  line,  each 
H  atom  uniting  with  the  Cl  atom  belonging  to  the  neighbour- 
ing molecule,  a  +  half  molecule  of  hydrogen  being  liberated 
at  the  kathode,  and  a  —  half  molecule  of  chlorine  at  the  anode. 
This  action  would  leave  the  molecules  as  in  the  third  row, 
and  would,  when  repeated,  result  in  a  double  migration  of 
hydrogen  atoms  in  one  direction  and  of  chlorine  atoms  on 
the  other ;  the  free  atoms  appearing  only  at  the  electrodes, 
and  every  atom  so  liberated  discharging  a  certain  definite 
minute  charge  of  electricity  upon  the  electrode  where  it  was 
liberated.1 

1  Johnstone  Stoney  reckoned,  from  considerations  founded  on  the  size  of 
atoms  (as  calculated  by  Loschmidt  and  Lord  Kelvin) ,  that  for  every  chemical 


560  ELECTRICITY   AND   MAGNETISM     [PT.  n.  570 

Clausius  sought  to  bring  the  ideas  of  Grotthuss  into  con- 
formity with  the  modern  kinetic  hypothesis  of  the  constitu- 
tion of  liquids.  He  supposes  that  in  the  usual  state  of  a 
liquid  the  molecules  are  always  gliding  about  amongst  one 
another,  and  their  constituent  atoms  are  also  in  movement, 
continually  separating  and  recombining  into  similar  groups, 
their  movements  taking  place  in  all  possible  directions 
throughout  the  liquid.  But  under  the  influence  of  an  elec- 
tromotive-force these  actions  are  controlled  in  direction,  so 
that  when,  in  the  course  of  the  usual  movements,  an  atom 
separates  from  a  group  it  tends  to  move  either  toward  the 
anode  or  kathode ;  and  if  the  electromotive-force  in  question 
be  powerful  enough  to  prevent  recombination,  these  atoms 
will  be  permanently  separated,  and  will  accumulate  around 
the  electrodes.  This  theory  has  the  advantage  of  account- 
ing for  a  fact  easily  observed,  that  an  electromotive-force 
kss  than  the  minimum  which  is  needed  to  effect  complete 
electrolysis  may  send  a  feeble  current  through  an  electrolyte 
for  a  limited  time,  until  the  opposing  electromotive-force  has 
reached  an  equal  value.  Von  Helmholtz,  who  gave  the 
name  of  electrolytic  convection  to  this  phenomenon  of  partial 
electrolysis,  assumed  that  it  takes  place  by  the  agency  of 
uncombined  atoms  previously  existing  in  the  liquid.  Arrhe- 
nius,  in  1884,  made  the  further  suggestion  that  in  every  dilute 
solution  of  any  acid  or  salt,  the  great  majority  of  the  mole- 
cules so  dissolved  are  "  ionized,"  that  is,  split  up  into  their 
respective  free  ions ;  and  the  more  dilute  the  solution  the 
more  complete  the  ionization.  All  conduction  in  electrolytes 
is  due  exclusively  to  the  carrying  of  electricity  by  these  free 
ions.  Kohlrausch  found  that  specially  purified  water  does 

bond  ruptured,  a  charge  of  1  X  10~19  of  a  coulomb  is  transferred.  [E. 
Budde  says  1.7  X  10~19  coulomb.]  This  quantity  would  appear  to  be  the 
natural  atomic  charge  or  electron.  (See  Art.  630.)  To  tear  one  atom  of 
hydrogen  from  a  hydrogen  compound  this  amount  of  electricity  must  be 
sent  through  it.  To  liberate  an  atom  of  zinc,  or  any  other  divalent  metal 
from  its  compound,  implies  the  transfer  of  twice  this  amount  of  electricity. 
See  Art.  256,  p.  222. 


CH.  xm.  571]        MIGRATION  OF  THE   IONS 


561 


not  conduct  at  all :  it  contains  no  free  ions.  But  if  as  little  as 
half  of  1  per  cent  of  hydrochloric  acid  or  of  sulphuric  acid  is 
added,  it  conducts  well,  for  at  that  dilution  99  per  cent  of 
the  acid  molecules  are  ionized  and  act  as  carriers. 

571.  Migration  of  the  Ions.  —  So  far  as  explained  it 
might  be  supposed  that  the  migration  of  the  constituents 
along  the  molecular  chains  during  electrolysis  was  merely 
a  continually  repeated  exchange  of  partners  between  the 
two  sets  of  ions,  the  anions  and  kations  travelling  thus  at 
equal  rates,  in  opposite  directions,  toward  the  anode  and 
kathode  respectively.  There  are,  however,  some  addditional 
facts  to  be  observed  by  experiment 
which  indicate  that  the  anions  and 
kations  travel  at  different  rates,  and 
that  each  ion  has,  under  given  circum- 
stances, its  own  specific  rate  of  migrat- 
ing. Hittorf,  who  first  drew  attention 
to  these  facts,  tabulated  the  observed 
ionic  velocities.  Since  then  Kohl- 
rausch,  Arrhenius,  Ostwald  and  others 
have  shown  that  this  property  is  in- 
timately connected  with  the  conduc- 
tivity of  the  electrolyte,  and  with  the 
phenomena  of  solubility,  of  osmotic 
pressure,  and  of  vapour-pressure.  In 
fact,  a  whole  new  chapter  of  electro- 
chemistry has  thus  been  opened  out. 

The  fundamental  experiment  upon 
which  is  based  the  modern  conception    FIG.  336.  —  Experiment  on 
of  the  velocity  of  migration  of  the  ions         Migration  of  IOM. 
is  an  exceedingly  simple  one.     Let  a  simple  glass  tube  about 
a  foot  long  and  one  inch  in  internal  diameter  be  provided 
with  well-fitting  corks  at  its  two  ends,  as  in  Fig.  336.     In 
this  is  placed  a  nearly  concentrated  and  slightly  acidified 
solution  of  copper  sulphate  to  be  electrolysed.     Through  the 
corks  pass  two  stout  copper  wires  each  furnished  at  the  end 
2o 


562  ELECTRICITY  AND  MAGNETISM      [PT.  n.  571 

with  a  round  disk  of  sheet-copper,  perforated  with  holes  to 
permit  of  circulation  of  liquid.  The  upper  one  k,  which 
serves  as  kathode,  is  just  immersed  below  the  surface  of  the 
liquid ;  the  other  a,  which  is  the  anode,  is  placed  two  or  three 
inches  lower  down  in  the  liquid.  The  current  from  a  few 
cells  of  battery  is  then  sent  upwards  through  the  electrolyte, 
the  current  being  so  regulated  that  it  is  not  too  strong,  other- 
wise bubbles  of  gas  will  be  given  off  and  disturb  the  experi- 
ment. Copper  will,  of  course,  be  plated  upon  the  upper  or 
kathode  plate,  an  equal  amount  of  copper  being  dissolved  off 
the  lower  or  anode  plate.  After  half  an  hour  or  so  it  will  be 
seen  that,  immediately  under  the  kathode,  the  blue  liquid 
has  become  quite  colourless,  and  if  the  experiment  is 
continued,  the  surface  of  separation  between  the  colourless 
liquid  at  the  top  and  the  blue  liquid  below  it  will  be  found  to 
have  moved  steadily  downward.  (If  the  current  is  sent 
downwards  no  such  phenomenon  can  be  seen,  owing  to  the 
descent  by  gravity  of  the  heavier  blue  liquid.)  The  colourless 
liquid  is  simply  water  slightly  acidulated.  There  are  two 
ways  of  explaining  that  which  has  occurred.  One  is  that, 
in  some  way,  in  addition  to  the  ordinary  electrolysis  in  which 
the  ions  Cu  and  SO4  have  been  transferred  in  opposite  direc- 
tions, there  has  been  a  bodily  transfer  toward  the  anode  of  the 
CuSO4  which  was  in  solution.  The  other  mode  of  explana- 
tion is  that  the  ions  Cu  and  SCX  have  travelled  with  different 
velocities ;  the  Cu  travelling  upward  more  slowly  than  the 
864  downward.  In  the  diagrams  to  the  left  and  right  of 
the  apparatus  in  Fig.  336  are  shown  some  rows  of  dots  for 
the  purpose  of  illustrating  the  relative  numbers  of  the  ions 
in  the  upper  and  lower  parts  of  the  liquid.  The  black 
dots  show  the  kations  (Cu),  and  the  white  ones  the  anions 
(804).  Before  electrolysis  begins  the  solution  is  uniform, 
as  shown  on  the  left;  there  being  9  anions  and  9  kations 
(that  is  9  of  CuSO4)  in  each  part,  upper  and  lower.  Sup- 
pose that  electrolysis  has  gone  on  for  so  long  a  time  that  6 
of  the  kations  have  been  dissociated  and  plated  on  the 


CH.  xiii.  571]        MIGRATION   OF   THE   IONS  563 

upper  disk,  and  that  6  of  the  anions  have  been  likewise  liber- 
ated and  carried  down  to  the  anode,  there  to  combine  with 
fresh  copper.  Now,  if  the  observed  state  of  things  is  repre- 
sented by  the  diagram  on  the  right,  it  will  be  seen  that  while 
in  the  upper  layer  there  are  5  CuS04  molecules,  in  the  lower 
there  are  7  CuSO4  molecules,  together  with  the  6  SO4  which 
have  gone  to  dissolve  fresh  copper.  If  the  migrations  of 
anions  and  kations  had  been  equal  there  would  have  been 
6CuS04  in  each  layer.  If  the  anions  alone  had  migrated, 
downwards,  there  would  have  been  15CuSO4  below  and 
3  CuS04  above.  If  the  kations  alone  had  moved,  upwards, 
there  would  have  been  9  CuS04  in  the  upper  layer,  leaving 
3  of  the  original  CuSO4  in  the  lower,  together  with  the  newly- 
formed  6  CuSO4.  If,  however,  the  diagram  on  the  right  rep- 
resents the  facts,  either  2  CuS04  must  have  been  bodily 
transferred  into  the  lower  layer  from  the  upper,  or  else  the 
transfer  of  ions  must  have  been  unequal,  4  anions  going 
downwards  into  the  lower  layer,  while  2  kations  have  gone 
upward  into  the  upper  layer.  In  other  words,  f  or  0-33  of 
the  total  displacement  has  been  that  of  the  copper  ions 
while  |  or  0-66  has  been  that  of  the  SO4  ions.  These  numbers 
Hittorf  called  the  migration  constants :  they  state  the  relative 
velocities  with  which  the  ions  migrate.  The  numbers  vary 
with  the  concentration  of  the  solution.  Thus,  in  the  case 
of  copper  sulphate,  if  the  solution  contains  2  gramme- 
equivalents  per  litre  the  migration  constant  for  the  anion 
is  about  0-725,  while  if  it  contain  only  YV  as  much  per  litre 
the  constant  falls  to  0-638.  If  this  number  for  the  anion  be 
called  n,  then  that  of  the  kation  will  obviously  be  1  —  n. 
If  we  denote  by  u  and  v  the  actual  velocities  with  which  the 
kations  and  anions  respectively  travel  under  a  potential 
gradient  of  1  volt  per  centimetre  of  length  of  the  electrolyte, 
we  clearly  may  write  the  equation 

u  _  1  —  nt 
v        n 


564  ELECTRICITY  AND   MAGNETISM      [PT.  n.  571 

Further,  the  relative  velocity  of  the  ions  past  one  another 
will  be  u  +  v.  If  by  using  a  stronger  battery  we  cause  a 
greater  fall  of  potential  than  1  volt  per  centimetre,  the  actual 
velocities  will  be  proportionally  greater,  but  the  ratio  of  u  to 
v  will  remain  as  before.  The  actual  velocities  u  and  v  Kohl- 
rausch  deduced  from  the  specific  conductivities  of  the  liquids. 
For  if  0-00001044  gramme  be  the  electro-chemical  equiva- 
lent of  hydrogen,  and  if  there  be  N  gramme-equivalents  of 
the  dissolved  electrolyte  in  one  cubic  centimetre  of  the  solu- 
tion, then  N  -f-  0-00001044  will  be  the  number  of  coulombs  of 
electricity  concerned  in  electrolysing  this  amount  of  the 
solution ;  and  if  the  ions  are  dragged  past  one  another 
with  a  speed  of  u  +  v  (centimetres  per  second)  the  flow  of 
electricity  in  one  second  across  unit  area  will  be  (u  -f  t>)N 
-s-  0-00001044  ampere.  Now  if  the  fall  of  potential  across 
a  length  of  x  centimetres  be  called  V,  the  potential  gradient 
being  therefore  V  -f-  x,  the  current  will  be  equal  to  this  mul- 
tiplied by  the  specific  conductivity  k ;  and  equating  these  we 
have  —  7  v 

u+-v  =  0-00001044^--; 

IS      x 

or  for  a  potential  gradient  of  1  volt  (=  108C.G.S.)  per  centi- 
metre    7 

u  +  v  =1044^; 

or  finally  —  , 

u  +  v  =1044000-, 

n 

where  n  is  the  number  of  gramme-equivalents  per  litre. 
Kohlrausch  determined  the  values  of  the  molecular  con- 
ductivity k  -7-  n  for  many  solutions.  He  found  it  to  increase 
with  dilution ;  becoming  constant  for  each  salt  at  very  ex- 
treme dilutions.  He  also  found  that  the  values  of  this  veloc- 
ity came  out  the  same  for  the  same  ion  when  used  in  different 
chemical  combinations.  Thus  for  hydrogen  at  18°  C.  and 
under  a  gradient  of  1  volt  per  centimetre,  the  ionic  velocity 
is  0-00323  centimetre  per  second;  that  of  sodium  0-00045; 
that  of  silver  0-00058. 


CH.  xiii.  572] 


ACCUMULATORS 


565 


LESSON  LII.  —  Accumulators 

572.  Accumulators  or  Secondary  Batteries. — A  voltam- 
eter, or  series  of  voltameters,  whose  electrodes  are  charged 
respectively  with  hydrogen  and  oxygen,  will  serve  as  second- 
ary batteries,  in  which  the  energy  of  a  current  may  be  stored 
up  and  again  given  out.  Ritter,  who  in  1803  constructed  a 
secondary  pile,  used  electrodes  of  platinum.  It  will  be  seen 
that  such  cells  do  not  accumulate  or  store  electricity ;  what 
they  accumulate  is  energy,  which  they  store  in  the  form  of 
chemical  work.  A  secondary  cell  resembles  a  Ley  den  jar  in 
that  it  can  be  charged  and  then  dis- 
charged. The  residual  charges  of 
Ley  den  jars,  though  small  in  quantity 
and  transient  in  their  discharge,  yet  ex- 
actly resemble  the  polarization  charges 
of  voltameters.  Varley  found  1  sq. 
centim.  of  platinum  foil  in  dilute  acid 
to  act  as  a  condenser  of  about  63  micro- 
farads' capacity,  when  polarized  to  a 
potential  difference  of  1  volt.  Gaston 
Plante,  in  1860,  devised  a  secondary  cell 
consisting  of  two  pieces  of  sheet  lead 
rolled  up  (without  actual  contact)  as 
electrodes,  dipping  into  dilute  sulphuric 
acid,  as  in  Fig.  337.  To  "  form  "  or 
prepare  the  lead  it  was  charged  with 
currents  which  after  a  time  were  re- 
versed in  direction,  and  after  a  further 
time  again  reversed,  until,  after  several 
reversals,  it  became  coated  with  a  semi- 
porous  film  of  brown  dioxide  of  lead  on  the  anode  plate ;  the 
kathode  plate  assuming  a  spongy  metallic  state  presenting  a 
large  amount  of  surface  of  high  chemical  activity.  When 
such  a  secondary  battery,  or  accumulator,  »is  charged  by  con- 
necting it  with  a  dynamo  (shunt- wound),  or  other  powerful 


FIG.  337.  —  Plant's 
Accumulator. 


566  ELECTRICITY  AND   MAGNETISM      [PT.  n.  572 

generator  of  currents,  the  anode  plate  becomes  peroxidized, 
while  the  kathode  plate  is  deoxidized  by  the  hydrogen  that  is 
liberated.  The  plates  may  remain  for  many  days  in  this  con- 
dition, and  will  furnish  a  current  until  the  two  lead  surfaces 
are  reduced  to  a  chemically  inactive  state.  The  electro- 
motive-force of  such  cells  is  from  2-0  to  1-85  volts  during  dis- 
charge. Plante  ingeniously  arranged  batteries  of  such  cells  so 
that  they  can  be  charged  in  parallel,  and  discharged  in  series, 
giving  (for  a  short  time)  strong  currents  at  extremely  high 
voltages.  Faure,  in  1881,  modified  the  Plante  accumulator 
by  giving  the  two  lead  plates  a  preliminary  coating  of  red- 
lead  (minium).  When  a  current  is  passed  through  the  cell 
to  charge  it,  the  red-lead  is  peroxidized  at  the  anode,  and 
reduced  —  first  to  a  condition  of  lower  oxide,  then  to  the 
spongy  metallic  state  —  at  the  kathode,  and  thus  a  greater 
thickness  of  the  working  substance  is  provided,  and  takes  far 

less  time  to  "  form  "  than  is  the 
case  with  Planters  cells.  In 
modern  accumulators  the  red- 
lead  (or  litharge),  freshly  mixed 
with  dilute  sulphuric  acid  to  the 
form  of  a  paste,  is  pressed  into  the 
holes  of  a  leaden  grid,  shaped  so 
as  to  give  it  a  good  mechanical 
attachment.  During  the  sub- 
sequent process  of  "  formation  " 
the  hardened  paste  is  reduced  on 

FIG.  assT^Ceii  of  Secondary        one  plate  (the  "  negative  ")  and 

peroxidized    on    the    other    (the 

"  positive  ").  A  cell  of  the  kind  known  as  the  E. P. S.  cell  is 
shown  in  Fig.  338.  Positive  plates  for  accumulators  are 
still  made  on  the  Plante  method  from  metallic  lead,  which 
is  first  made  into  ribbons  or  powder  and  packed  into  inter- 
stices in  a  metallic  grid,  and  then  "  peroxidized  "  by  pro- 
longed charging.  Cells  of  this  type  are  not  so  subject  to  dis- 
integration as  paste  cells,  and  may  be  discharged  at  a  greater 


CH.  xiii.  573, 574]  ACCUMULATORS  567 

rate.  To  keep  accumulators  in  good  condition  they  should 
be  charged  up  every  day  till  full  (known  by  bubbles  rising) 
and  not  be  discharged  too  quickly.  The  density  of  acid 
should  never  be  allowed  to  exceed  1-21  nor  fall  below  1*15. 
The  average  number  of  amperes  which  a  cell  discharges 
multiplied  by  the  hours  which  the  discharge  lasts,  is  called 
its  "  ampere-hours."  If  the  rate  of  discharge  is  increased, 
the  number  of  ampere-hours  is  lowered.  Stationary  accumu- 
lators will  give  from  25  to  33  watt-hours  per  kilogramme  of 
total  weight :  portable  accumulators  about  6  to  10.  The 
efficiency  is  between  75  and  80  per  cent. 

573.  Edison's   Accumulator.  —  In   this   cell  the   positive 
plate  consists  of  hydrated  oxide  of  nickel  packed  into  a  steel 
grid,  and  the  negative  of  finely  divided  iron  also  packed  into 
a  grid.     The  cell  is  filled  with  a  solution  of  caustic  potash. 
During  discharge  the  iron  is  oxidized  and  the  nickel  oxide 
partially  reduced.     During  charging  the  chemical  actions 
are  reversed.     The  storage  is  about  20  watt-hours  per  kilo- 
gramme of  total  weight.     The  cells  are  lighter,  and  more 
mechanical  than  the  cells  of  lead  batteries,  and  they  may  be 
charged  more  rapidly.     But  the  cell  has  only  about  1-25 
volts  of  electromotive-force,  and  the  efficiency  is  not  more 
than  50  per  cent. 

574.  Grove's  Gas  Battery.  —  Sir  W.  Grove  devised  a  cell 
in  which  platinum  electrodes,  in  contact  respectively  with 
hydrogen  and  oxygen  gas,  replaced  the  usual  zinc  and  copper 
plates.     Each  of  these  gases  is  partially  occluded  by  the  metal 
platinum,  which,  when  so  treated,  behaves  like  a  different 
metal. 

Attempts  have  been  made  to  generate  electricity  on  a 
larger  scale  by  means  of  gas  batteries.  Mond  and  Lange 
found  that  the  greatest  E.M.F.  to  be  obtained  from  a  cell  of 
hydrogen  and  oxygen,  with  finely-divided  platinum  as  col- 
lectors, was  0-97,  the  difference  between  this  and  the  theoreti- 
cal 149,  being  lost  in  heat  generated  by  the  condensation  of 
the  gases  by  the  platinum. 


568          ELECTRICITY  AND   MAGNETISM    [PT.  n.  575,  576 


LESSON  LIII.  —  Electrodeposition 

575.  Electrometallurgy.  —  The    applications    of    electro- 
chemistry to  the  industries  are  threefold.     First,  to  the  re- 
duction of  metals  from  solutions  of  their  ores ;    secondly,  to 
the   copying   of   types,    plaster-casts,    and   metal-work   by 
kathode  deposits  of  metal ;  thirdly,  to  the  covering  of  objects 
made  of  baser  metal  with  a  thin  film  of  another  metal,  such 
as  gold,  silver,  or  nickel.     All  these  operations  are  included 
under  the  general  term  of  electrometallurgy.     The  same  term 
is  used  loosely  to  include  the  operation  both  of  electric  fur- 
naces (Art.  469)  in  which  the  operations  are  thermal  and  of 
those  in  which  they  are  electrolytic  (Art.  579). 

Copper  of  a  high  degree  of  purity  is  refined  on  a  large 
scale  by  suspending  anodes  of  impure  copper  in  a  solution 
of  copper  sulphate  and  electrolytically  depositing  pure  copper 
on  the  kathodes.  The  impurities  such  as  arsenic,  being  more 
electronegative  than  copper,  are  left  behind  as  a  sludge  in 
the  bath. 

576.  Electrotyping.  —  In  1836  De  la  Rue  observed  that 
in  a  Daniell's  cell  the  copper  deposited  out  of  the  solution 
upon  the  copper  plate  which  served  as  a  kathode  took  the 
exact  impress  of  the  plate,  even  to  the  scratches  upon  it. 
In   1839  Jacobi  in  Petrograd,   Spencer  in   Liverpool,   and 
Jordan  in  London,  independently  developed  out  of  this  fact 
a  method  of  obtaining,  by  the  electrolysis  of  copper,  impres- 
sions (in  reversed  relief)  of  coins,  stereotype  plates  and  orna- 
ments.    A  further  improvement,  due  to   Murray,  was  the 
employment  of  moulds  of  plaster  or  wax,  coated  with  a 
film  of  plumbago  in  order  to  provide  a  conducting  surface 
upon  which  the  deposit  could  be  made.     Bronze  in  the  form 
of  a  fine  powder  is  much  used  instead  of  plumbago,  being  a 
better  conductor.     Jacobi  gave  to  the  process  the  name  of 
galvanoplastic,  a  term  generally  abandoned  in  favour  of  the 
term  electrotyping  or  electrotype  process. 


CH.  xm.  577]  ELECTRODEPOSITION  569 

Electrotypes  of  copper  are  easily  made  by  hanging  a 
suitable  mould  in  a  cell  containing  a  nearly  saturated  and 
slightly  acidulated  solution  of  sulphate  of  copper,  and  passing 
a  current  of  a  battery  through  the  cell,  the  mould  metallized 
on  its  surface  being  the  kathode,  a  plate  of  copper  being 
employed  as  an  anode,  dissolving  gradually  into  the  liquid 
at  a  rate  exactly  equal  to  the  rate  of  deposition  at  the 
kathode.  This  use  of  a  separate  cell  or  "  bath  "  is  more 
convenient  than  producing  the  electrotypes  in  the  actual  cell 
of  a  Daniell's  battery.  The  process  is  largely  employed  at 
the  present  day  to  reproduce  repousse  and  chased  ornament 
and  other  works  of  art  in  facsimile,  and  to  multiply  copies 
of  wood  blocks  for  printing.  Almost  all  the  illustrations  in 
this  book,  for  example,  are  printed  from  electrotype  copies, 
and  not  from  the  original  wood  blocks,  which  would  not  wear 
so  well.  In  all  deposition  processes  success  largely  depends 
on  having  the  proper  current-density.  To  deposit  metals 
that  are  more  positive  than  hydrogen,  such  as  zinc  or  chro- 
mium, it  is  advisable  to  use  concentrated  solutions  and  high 
current-densities.  For  metals  that  are  less  positive,  such 
as  copper  and  silver,  the  current-density  may  be  less.  To 
procure  a  good  tough  deposit  of  copper  the  current  should 
not  exceed  15  amperes  per  square  foot  of  kathode  surface. 
If  a  more  rapid  deposit  is  required,  a  solution  of  nitrate  of 
copper  should  be  used  and  kept  in  rapid  agitation. 

To  deposit  iron  (by  the  process  known  as  acierage,  or  steel- 
facing)  a  very  large  sheet  of  iron  is  used  as  anode,  and  the 
liquid  used  is  simply  a  solution  of  salammoniac  in  water. 
This  solution  is  "  charged  "  with  iron  by  passing  the  current 
for  a  little  time  through  the  bath  prior  to  inserting  the  object 
to  be  steel-faced. 

577.  Electroplating.  —  In  1801  Wollaston  observed  that 
a  piece  of  silver,  connected  with  a  more  positive  metal,  be- 
came coated  with  copper  when  put  into  a  solution  of  copper. 
In  1805  Brugnatelli  gilded  two  silver  medals  by  making  them 
the  kathodes  of  a  cell  containing  a  solution  of  gold.  Messrs. 


570 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  577 


Elkington,  about  the  year  1840,  introduced  the  commercial 
processes  of  electroplating.  In  these  processes  a  baser  metal, 
such  as  german  silver  (an  alloy  of  zinc,  copper,  and  nickel), 
is  covered  with  a  thin  film  of  silver  or  gold;  the  solutions 
employed  being,  for  electro-gilding,  the  double  cyanide  of 
gold  and  potassium,  and  for  electro-silvering  the  double  cya- 
nide of  silver  and  potassium'.  According  to  Hittorf  the 
double  cyanide  KAgCy2  is  ionized  into  K  and  AgCy2 ;  the 


FIG.  339.  —  Silver-Plating  by  means  of  a  Primary  Cell. 

potassium  ion  then  reacting  on  another  molecule  of  cyanide 
according  to  the  equation  K  +  KAgCy2  =  2  KCy  +  Ag. 

Fig.  339  shows  a  primary  cell  and  a  plating- vat  containing 
the  silver  solution.  As  anode  is  hung  a  plate  of  metallic 
silver  which  dissolves  into  the  liquid.  To  the  kathode  are 
suspended  the  spoons,  forks,  or  other  articles  which  are  to 
receive  a  coating  of  silver.  The  addition  of  a  minute  trace 
of  bisulphide  of  carbon  to  the.  solution  causes  the  deposited 
metal  to  have  a  bright  surface.  If  the  current  is  too  strong, 
and  the  deposition  too  rapid,  the  deposited  metal  is  grayish 
and  crystalline. 

In  gilding  base  metals,  such  as  pewter,  they  are  usually 
first  copper-coated.  The  gilding  of  the  insides  of  jugs  and 
cups  is  effected  by  filling  the  jug  or  cup  with  the  gilding  solu- 
tion, and  suspending  in  it  an  anode  of  gold,  the  vessel  itself 
being  connected  to  the  —  pole  of  the  battery. 


CH.  xiii.  578, 579]      ELECTROLYTIC    FURNACES  571 

In  silvering  or  gilding  objects  of  iron  it  is  usual  first  to 
plate  them  with  a  thin  coating  of  copper  deposited  from  an 
"  alkaline  "  copper  bath  containing  an  ammoniacal  solu- 
tion of  cyanide  of  copper.  Brass  is  deposited  also  from  an 
ammoniacal  solution  of  the  mixed  cyanides  of  copper  and 
zinc.  In  the  deposition  of  nickel  a  solution  of  the  double 
sulphate  of  nickel  and  ammonium  is  used,  the  anode  being 
a  sheet  of  rolled  (or  cast)  nickel. 

Except  on  the  very  small  scale,  batteries  are  now  seldom 
used  for  electrotyping  and  plating.  A  shunt-wound  dynamo 
designed  to  give  a  large  current  at  the  low  pressure  of  5  to  10 
volts  pressure  is  generally  preferred. 

578.  Other     Electrolytic     Processes.  —  The     electrolytic 
action  of  the  current  is  now  commercially  employed  for  other 
purposes  than  the  deposition  of  metals.     By  the  electrolysis 
of  chloride  of  potassium  under  suitable  conditions  chlorate  of 
potash  is  now  manufactured  in  large  quantities.     Bleaching 
liquors  containing  hypochlorites  can  also  be  produced  from 
chlorides.      Caustic    soda    is    prepared    by    electrolysis    of 
common  salt ;  and  several  electrolytic  methods  of  disinfect- 
ing sewage  are  in  use. 

It  has  also  been  shown  that  the  slow  processes  of  tanning 
can  be  accelerated  by  the  acid  of  electric  currents,  the 
action  being  probably  osmotic  rather  than  electrolytic. 

It  seems  probable  that  in  the  future  the  use  of  electric 
currents  will  enter  largely  into  the  chemical  manufactures. 

579.  Electrolytic  Furnaces.  —  If  two  stout  rods  of  carbon 
are  introduced  into  a  crucible  lined  with  magnesia  or  other 
refractory  substance,  and  an  arc  (Art.  486)  is  formed  between 
them,  the  internal  temperature  exceeds  that  of  any  other 
artificial  source,  enabling  many  chemical  actions  to  be  pro- 
duced that  are  otherwise  unattainable.     Thus  if  lime  mixed 
with  coke  is  heated  in  the  electric  furnace  there  is  produced 
calcium  carbide,  CaC2,  which  when  mixed  with  water  yields 
acetylene  gas.     Many  most  refractory  compounds,  such  as 
the  oxides  of  titanium  and  chromium,  can  thus  be  reduced. 


572  ELECTRICITY  AND   MAGNETISM         [PT.  n.  579 

Pure  aluminium  is  now  produced  in  large  quantities  by 
the  electrolysis  of  fused  cryolite,  which  is  a  double  fluoride 
of  aluminium  and  sodium ;  pure  alumina  being  added  from 
time  to  time.  In  another  process  aluminium  oxide  is  mixed 
with  charcoal  and  placed  between  the  ends  of  two  thick 
carbon  rods  in  a  closed  fire-brick  furnace  lined  with  charcoal. 
A  current  of  several  thousand  amperes  is  passed  between 
the  carbon  rods,  and  the  aluminium  ore  is  melted  and  parts 
with  its  oxygen  to  carbon.  The  liberated  aluminium  may  be 
allowed  to  alloy  with  some  other  metal,  such  as  copper,  or  it 
will  combine  with  the  carbon  present  and  form  a  carbide.  It 
is  practically  impossible  to  obtain  pure  aluminium  by  this 
process. 

In  another  kind  of  electric  furnace,  invented  by  Birke- 
land  and  Eyde,  nitric  acid  is  produced  by  passing  atmos- 
pheric air  through  a  high- voltage  alternating  arc  between  the 
poles  of  a  magnet.  In  this  case  the  arc  becomes  an  endo- 
thermic  flame,  absorbing  energy,  and  causing  the  chemical 
combination  of  nitrogen  with  oxygen.  The  nitric  oxides  so 
produced  are  absorbed  into  water  to  form  nitric  acid,  or 
neutralized  with  lime  to  form  nitrate  of  lime  as  a  fertilizer. 
This  process  has  become  the  basis  of  a  large  industry,  using 
electric  power,  generated  on  a  large  scale  by  waterfalls  work- 
ing water  turbines. 


CHAPTER  XIV 

TELEGRAPHY 

LESSON  LIV.  —  Electric  Telegraphs 

580.  The  Electric  Telegraph.  —  It  is  difficult  to  assign 
the  invention  of  the  telegraph  to  any  particular  inventor. 
Lesage  (Geneva,  1774),  Lomond  (Paris,  1787),  and  Sir  F. 
Ronalds  (London,  1816)  invented  systems  for  transmitting 
signals  through  wires  by  observing  at  one  end  the  divergence 
of  a  pair  of  pith-balls  when  a  charge  of  electricity  was  sent 
into  the  other  end.  Cavallo  (London,  1795)  transmitted 
sparks  from  Leyden  jars  through  wires  "  according  to  a 
settled  plan."  Soemmering  (Munich,  1808)  established  a 
telegraph  in  which  the  signals  were  made  by  the  decomposi- 
tion of  water  in  voltameters ;  and  the  transmission  of  signals 
by  the  chemical  decomposition  of  substances  was  attempted 
by  Coxe,  R.  Smith,  Bain,  and  others.  Ampere  (Paris,  1821) 
suggested  that  a  galvanometer  placed  at  a  distant  point  of  a 
circuit  might  serve  for  the  transmission  of  signals.  Schilling 
and  Weber  (Gottingen,  1833)  employed  the  deflexions  of  a 
galvanometer  needle  moving  to  right  or  left  to  signal  an 
alphabetic  code  of  letters  upon  a  single  circuit.  Cooke 
and  Wheatstone  (London,  1837)  brought  into  practical  appli- 
cation the  first  form  of  their  needle  telegraph.  Henry  (New 
York,  1831)  utilized  the  attraction  of  an  electromagnet  to 
transmit  signals,  the  movement  of  the  armature  producing 
audible  sounds  according  to  a  certain  code.  Morse  (New 
York,  1837)  devised  a  telegraph  in  which  the  attraction  of  an 
armature  by  an  electromagnet  was  made  to  mark  a  dot  or  a 
dash  upon  a  moving  strip  of  paper.  Steinheil  (Munich,  1837) 

573 


574  ELECTRICITY   AND   MAGNETISM      [PT.  n.  581 

discovered  that  instead  of  a  return-wire  the  earth  might  be 
used,  contact  being  made  to  earth  at  the  two  ends  by  means 
of  earth-plates  (see  Fig.  343  6)  sunk  in  the  ground.  Gintl 
(1853)  and  Stearns  (New  York,  1870)  devised  methods  of 
duplex  signalling.  Stark  (Vienna)  and  Bosscha  (Leyden, 
1855)  invented  diplex  signalling,  and  Heaviside  (London, 
1873)  and  Edison  (Newark,  N.J.,  1874)  invented  quadruplex 
telegraphy.  Varley  (London,  1870)  and  Elisha  Gray 
(Chicago,  1874)  devised  harmonic  telegraphs.  For  fast- 
speed  work  Wheatstone  devised  his  automatic  transmitter, 
in  which  the  signs  which  represent  the  letters  are  first  punched 
by  machinery  on  strips  of  paper ;  these  are  then  run  at  a  great 
speed  through  the  transmitting  instrument,  which  telegraphs 
them  off  at  a  much  greater  rate  than  if  the  separate  signals 
were  telegraphed  by  hand.  Hughes  devised  a  type-printing 
telegraph.  Wheatstone  invented  an  ABC  telegraph  in  which 
signals  are  spelled  by  a  hand  which  moves  over  a  dial.  Cow- 
per  (1876)  and  Elisha  Gray  (1893)  invented  autographic  writ- 
ing telegraphs.  For  cable-working  Lord  Kelvin  invented 
his  mirror  galvanometer  and  his  delicate  siphon-recorder. 
It  is  impossible  in  these  Lessons  to  describe  more  than  one 
or  two  of  the  simple  ordinary  forms  of  telegraph  instrument 
now  in  use  in  Great  Britain.  For  further  information  con- 
sult Prescott's  Electricity  and  the  Electric  Telegraph;  or 
for  British  telegraphs,  the  manuals  of  Culley  or  of  Preece  and 
Sivewright. 

581.  Single-Needle  Instrument.  —  The  single-needle  in- 
strument (Fig.  340)  consists  essentially  of  a  vertical  galva- 
nometer, in  which  a  lightly-hung  magnetic  needle  is  deflected 
to  right  or  left  when  a  current  is  sent,  in  one  direction  or  the 
other,  around  a  coil  surrounding  the  needle ;  the  needle  vis- 
ible in  front  of  the  dial  is  but  an  index,  the  real  magnetic 
needle  being  behind.  A  code  of  movements  agreed  upon 
comprises  the  whole  alphabet  in  combinations  of  motions 
to  right  or  left.  In  order  to  send  currents  in  either  direction 
through  the  circuit,  a  "  signalling-key  "  or  "  tapper "  is 


CH.  xiv.  581]     SINGLE-NEEDLE    TELEGRAPH 


575 


usually  employed.  The  tapper  at  one  end  of  the  line  works 
the  instrument  at  the  other ;  but  for  the  sake  of  convenience 
it  is  fixed  to  the  receiving  instrument.  In  Fig.  340  the  two 
protruding  levers  at  the  base  form 
the  tapper,  and  by  depressing  the 
right-hand  one  or  the  left-hand  one, 
currents  are  sent  in  either  direction 
at  will. 

The  principle  of  action  will  be 
made  more  clear  by  reference  to 
Fig.  341,  which  shows  a  separate 
signalling  key.  The  two  horizontal 
levers  are  respectively  in  communi- 
cation with  the  "  line,"  and  with 
the  return-line  through  "  earth." 
When  not  in  use  both  levers  spring 
up  against  a  cross  strip  of  metal 
joined  to  the  zinc  pole  of  the  battery. 
is  another  cross  strip,  which  communicates  with  the  copper 
(or  +)  pole  of  the  battery.  On  depressing  the  "  line  " 
key  the  current  runs  through  the  line  and  back  by  earth, 


FIG.  340.  —  Single-needle 
Instrument. 


At  their  farther  end 


FIG.  341.  — Tapper  Signalling  Key. 


or  in  the  positive  direction.  On  depressing  the  "  earth  " 
key  (the  line-key  remaining  in  contact  with  the  zinc- 
connected  strip),  the  current  runs  through  the  earth  and 
back  by  the  line,  or  in  the  negative  direction.  Telegraphists 


576  ELECTRICITY  AND   MAGNETISM      [PT.  n.  582  a 

ordinarily  speak  of  these  as  positive  and  negative  currents 
respectively. 

582  a.  The  Morse  Instrument.  —  The  most  widely  used 
instrument  at  the  present  day  is  the  Morse.  It  consists 
essentially  of  an  electromagnet,  which,  when  a  current 
passes  through  its  coils,  draws  down  an  armature  for  a  short 
or  a  long  time.  It  may  either  be  arranged  as  a  "  sounder," 
in  which  case  the  operator  who  is  receiving  the  message 

listens  to  the  clicks,  and 
notices  whether  the  inter- 
vals between  them  are  long 
or  short;  or  it  may  be 
arranged  as  an  "  embosser," 
to  print  dots  and  dashes 
upon  a  strip  of  paper  drawn 
by  clockwork  through  the 
instrument.  In  the  most 

F,G.  342.  -  The  Morse  Sounder.  modem   f  ^^  however>  the 

Morse  instrument  is  arranged  as  an  "  ink-writer,"  in  which 
the  attraction  of  the  armature  downwards  lifts  a  little  inky 
wheel  and  pushes  it  against  a  ribbon  of  paper. 

The  Morse  Sounder,  which  is  almost  universal  in  the 
United  States,  and  is  being  increasingly  used  in  the  British 
Telegraph  Service,  is  depicted  in  Fig.  342.  In  this  instru- 
ment the  electromagnet  is  of  inverted  horseshoe  pattern, 
having  the  coils  wound  on  two  bobbins  which  are  slipped 
over  vertical  cores.  Above  the  poles  lies  an  iron  armature 
fixed  across  the  pivoted  lever.  Whenever  the  current 
passes  through  the  coils  the  armature  is  attracted  down, 
and  the  lever  makes  a  click  as  it  strikes  against  a  stop.  As 
soon  as  the  current  ceases  the  lever  is  raised  by  a  spring  and 
strikes  against  a  top  stop.  There  are  therefore  two  clicks 
heard.  When  a  "  dot  "  is  signalled  the  two  clicks  are  heard 
immediately  after  one  another.  When  a  "  dash"  is  signalled 
the  interval  between  the  clicks  is  longer.  With  a  little  prac- 
tice it  becomes  easy  to  read  the  sounder. 


CH.  xiv.  582  b]          MORSE    INSTRUMENT 


577 


The  Morse  Ink-  Writer,  as  used  in  the  British  Postal  Tele- 
graph Service,  is  depicted  in  Fig.  343  a.  A  piece  of  clock- 
work causes  a  ribbon  of  paper  (coiled  up  in  the  base  of  the 
instrument)  to  be  slowly  drawn  between  rollers,  while  the 
dots  and  dashes  are  printed  on  it  by  the  ink-wheel  affixed  to 
the  end  of  the  lever.  A  momentary  current  prints  a  mere  dot  ; 
but  if  the  current  continues  to  flow  for  a  longer  time  while 

LOCAL  BATTERY 


WRITER 


EARTH 

SENDING   BATTERY 
FIG.  343  a.  —  Morse  Writer,  with  Relay  and  Local  Circuit  (British  Pattern). 

the  ribbon  of  paper  moves  on,  the  ink-wheel  records  a  dash. 
The  connexions  show  how  the  instrument  is  worked  by  a 
local  battery  and  a  relay. 

582  b.    The  Morse  Alphabets.  —  The  international  Morse 
code,  or  alphabet  of  dots  and  dashes,  is  as  follows :  — 


A.— 
B— . 
C  — . 
D— . 
E  . 
F  ..- 
G  — 
H  ... 
I 


J 
K 
L 
M 

N 
O 
P 

Q 

R 


S 

T 

U 

V 

W 

X 

Y 

Z 


2p 


578 


ELECTRICITY  AND   MAGNETISM    [PT.  n.  582  c 


The  American  Morse  code,  originated  by  Morse  himself,  is 
used  only  in  the  United  States  and  Canada.  It  differs  in  many 
respects  from  the  International  code,  the  signals  for  some  of  the 
letters  depending  on  the  length  of  the  spacings  between  the  dots 
and  dashes;  and  more  than  four  marks  are  used  to  form  some 
of  the  letters.  The  marks  for  H,  Y,  and  Z  are  four  dots,  but  they 
are  differently  spaced.  The  following  is  the  American  Morse 
code : — 


A  .— 
B  — ... 
C  ..  . 
D  — .  . 
E  . 
F  .— . 

G . 

H.... 
I    .. 

J  — .  — . 
K  —  .— 
L 


M 

N  — . 
O  .  . 

P  

Q  ..-. 
R  .  .. 
S  ... 
T  — 
U  ..— 
V   ...— 

w  . — 

X  .  — .. 


Y 
Z 

1 
2 
3 
4 
5 
6 
7 
8 
9 
0 


582  c.   The    Morse    Key.  —  The   key   used   for  operating 
Morse  telegraphs.     The  American  pattern  differs  somewhat 

from  the  European 
pattern,  and  the 
mode  of  use  is  not 
precisely  the  same. 

The  general  ap- 
pearance  of  the 
American  pattern  of 
Morse  key  is  shown 
in  Fig.  343  b. 

The  key  is  fastened 
to  the  table  by  the 
screws  B  and  L, 

the  former  being  insulated  from  the  metal  base  and  lever, 
while  L  is  not  insulated.     One  wire  is  clamped  to  the  metal 


FIG.  343  b.  —  Morse  Key  (Standard  American  Pattern). 


CH.  xiv.  583]  MORSE   KEY  579 

of  the  key  at  L,  the  other  is  clamped  to  B.  The  lever,  which 
is  provided  with  a  finger-piece,  has  on  its  lower  side  a  short 
platinum  pin  just  above  the  head  of  the  screw  B,  so  that 
when  the  operator  depresses  the  lever  it  makes  contact  on  the 
head  of  the  screw  and  completes  the  circuit  from  B  to  L. 
The  range  of  motion  allowed  the  lever  is  regulated  by  a  screw- 
stop  in  the  further  end  of  the  lever.  Beside  the  parts  named 
the  key  is  usually  provided  with  a  switch,  shown  in  the  Fig. 
343  6  with  a  small  vertical  handle.  When  this  is  moved  to  the 
left  it  short-circuits  the  key,  and  puts  B  into  direct  con- 
nexion with  L.  When  moved  to  the  right,  the  circuit  is  open 
until  such  time  as  the  lever  is  depressed. 

The  Morse  key  as  used  in  the  British  telegraphs  is  depicted 
in  Fig.  343  c.  The  line  wire  is  connected  with  the  central 
pivot  A.  A  spring  keeps 
the  front  end  of  the  key 
elevated  when  not  in  use 
so  that  the  line  wire  is  in 
communication  through  the 
rear  end  of  the  key  with 
the  receiving  instrument  or 
relay.  Depressing  the  key  FlG" 343  c'  ~  Morse  Key  <Eur°Pean  Pattern>- 
breaks  this  communication,  and  by  putting  the  line  wire  in 
communication  with  the  sending  battery  transmits  a  current 
through  the  line. 

583.  Open-  and  Closed-circuit  Working.  —  European 
telegraphs  work  on  the  open-circuit  plan,  the  battery  being 
out  of  circuit  when  no  message  is  being  sent.  American 
telegraphs  are  usually  on  the  closed-circuit  plan,  the  current 
being  always  on  until  interrupted  to  send  signals.  Each 
plan  has  its  advantages.  The  closed-circuit  plan  enables 
a  way-line  to  unite  a  number  of  isolated  stations  all  in  a  single 
circuit,  each  one  of  which  can  signal  to  all  the  rest  by  opening 
the  circuit.  Further,  any  failure  in  the  line  immediately 
reports  itself  by  the  stoppage  of  the  current.  The  open- 
circuit  plan,  which  is  better  suited  for  communication  among 


580 


ELECTRICITY  AND   MAGNETISM         [PT.  n.  583 


MNE 


dense  populations,  and  for  all  lines  where  no  instruments 
are  wanted  to  be  inserted  at  intermediate  points,  has  the 
advantage  of  only  using  the  batteries  when  the  telegraph 
is  in  actual  use. 

In  the  open-circuit  plan  the  key  acts,  as  previously  de- 
scribed, merely  to  open  or  close  the  circuit.  The  general 
arrangement  of  apparatus  at  an  intermediate  or  "  way  " 
station  is  shown  in  Fig.  343  d.  The  current  coming  along 

the  line  enters  by  the 
line  wire  on  the  right 
and  comes  in  to  the 
metal  base  of  the  key  K, 
where  it  finds  a  passage 
along  the  switch  G 
(which  is  closed)  to  the 
head  H  of  the  screw 
(described  as  screw  B  of 
Fig.  3436).  Thence  it 
passes  to  the  relay  R, 
entering  it  at  the  ter- 
minal A,  passing  around 
the  electromagnet  M  of 

FIG.  343  d.  —  Morse  Sounder,  with  Relay  and  Local    +V»o    rvalair  •      anrl    icaninrr 
Circuit  (American  Pattern).  ^^  >     anClSSUing 

by  the    terminal  B   it 

passes  down  the  line  to  the  next  station.  This  current  is 
furnished  either  by  a  single  battery  inserted  in  the  line,  or 
by  two  batteries,  one  at  each  end  of  the  line  acting  in  the 
same  direction.  The  action  of  the  relay  is  considered  below. 
In  the  open-circuit  method,  as  it  is  necessary  that  a  line 
should  be  capable  of  being  worked  from  either  end,  a  battery 
is  used  at  each,  and  the  wires  so  connected  that  when  at  either 
end  a  message  is  being  received,  the  battery  circuit  at  that 
end  shall  be  open.  Fig.  344  shows  the  simplest  possible 
case  of  such  an  arrangement.  At  each  end  is  a  battery  zcy 
one  pole  of  which  is  put  to  earth,  and  the  other  communi- 
cates with  the  middle  point  of  a  Morse  key  K.  This  key  is 


CH.  xiv.  583]          OPEN-CIRCUIT   METHOD 


581 


arranged  (like  that  in  Fig.  343  c)  so  that  when  it  is  depressed 
to  send  a  signal  through  the  line  it  quits  contact  with  the 
receiving  instrument  at  its  own  end.  Both  ends  of  the  lever 
must  therefore  be  furnished  witji  contact-pins  of  platinum ; 
and  the  key  acts  as  a  two-way  key.  The  current  flowing 
through  the  line  passes  through  K'  and  enters  a  receiving 
instrument  G'  at  the  distant  end,  where  it  produces  a  signal, 
and  returns  by  the  earth  to  the  battery  whence  it  started. 
A  similar  battery  and  key  at  the  distant  end  suffice  to  trans- 


FIG.  344.  — Open-circuit  Signalling. 

mit  signals  in  the  opposite  direction  to  G  when  K  is  not  de- 
pressed. The  diagram  is  drawn  as  if  G  were  a  simple  gal- 
vanometer; but  the  arrangement  would  perfectly  suit  the 
Morse  instrument,  in  which  it  is  only  required  at  either 
end  to  send  long  and  short  currents  without  reversing  the 
direction,  as  with  the  needle  instruments.  In  this  diagram 
the  battery  current  is  never  reversed  and  the  method  is  known 
as  a  single-current  method.  There  is  a  so-called  double-cur- 
rent method  of  working,  in  which  reversing  keys  (resembling 
the  tapper  of  Fig.  341)  are  used  to  send  after  each  current  in 
the  positive  direction  a  second  current  in  the  negative  direc- 
tion. The  double-current  method  has  the  advantage  of 
enabling  the  signalling  to  be  more  rapid  on  long  lines  when  the 


582  ELECTRICITY  AND   MAGNETISM     [PT.  n.  584 

retardation  due  to  the  static  charging  of  the  line  is  of  impor- 
tance. The  second  current  helps  to  curb  the  first  and  makes 
the  signals  shorter  and  sharper. 

584.  Relays.  —  In  working  over  long  lines,  or  where  there 
are  a  number  of  instruments  on  one  circuit,  the  currents  are 
often  not  strong  enough  to  work  the  recording  instrument 
directly.  In  such  a  case  there  is  interposed  a  relay  or  repeater. 
This  instrument  consists  of  an  electromagnet  round  which 
the  line  current  flows,  and  whose  delicately  poised  armature, 
when  attracted,  makes  contact  for  a  local  circuit  in  which 
a  local  battery  and  the  receiving  Morse  instrument  (sounder, 
or  writer)  are  included.  The  principle  of  the  relay  is,  then, 
that  a  current  too  weak  to  do  the  work  itself  may  set  a  strong 
local  current  to  do  its  work  for  it. 

In  the  American  plan  of  working  (Fig.  343d),  the  relay 
is  a  simple  electromagnet  having  a  soft-iron  core,  and  an 

armature  of  iron  which 
it  attracts  whenever  a 
current  flows  round  its 
coils.  It  pulls  its  arma- 
ture no  matter  which 
way  the  current  flows. 
Such  a  non-polarized  re- 

FIG.  345  a.  —  Simple  Relay  (Western  Union        lay  of  the  Western  Union 

pattern   is    depicted   in 

Fig.  345  a.  Its  mode  of  operation  is  explained  by  the  dia- 
grammatic plan  of  Fig.  343  d.  Here  M  is  the  electromagnet, 
with  its  iron  armature  lightly  pivoted  at  P,  and  controlled 
by  the  spring  V.  When  any  current  passes,  the  light  lever 
or  tongue  on  which  the  armature  is  mounted  turns  on  its 
pivot  P,  and  makes  contact  against  the  stop  D,  thereby 
closing  a  local  circuit  DXLSYP,  which  includes  the  sounder 
S  and  a  local  battery  L. 

In  the  closed-circuit  method  of  working,  and  in  duplex 
telegraphy  "  polarized  relays  "  are  used,  which  will  respond 
to  currents  flowing  in  one  direction  only.  The  polarized 


CH.  xiv.  584] 


RELAYS 


583 


relay  of  Siemens's  pattern  is  shown  in  diagram  in  Fig.  345  b. 
In  it  a  permanently  magnetized  steel  magnet  is  employed  to 
produce  an  initial  magnetism  in  the  cores  of  the  electromag- 
net, and  in  the  pivoted  lever  or  tongue.  The  magnet  has  its 
S-pole  bent  up  at  right  angles  and  divided  so  that  the  tongue 
aD  of  the  relay,  which  is  of  iron,  may  be  thereby  polarized 
or  given  a  south  polarity.  Attached  to  the  N-pole  of  the 
magnet  are  the  two  cores,  over  which  the  two  bobbins  are 
slipped,  these  cores  ending  in  the  two  pole-pieces  marked  n,  n', 
which  are  of  northern  polarity.  They  both  attract  the 
tongue  that  lies 
between  them,  the 
nearer  one  pulling 
more  strongly.  If 
now  a  current  cir- 
culates round  the 
coils  it  will  tend  to 
strengthen  one  of 
the  poles  and 
weaken  the  other. 


If  it  flows  in  such 
a    direction    as    to 


a 


d 

TO  LOCAL 
BATTERY 


bg- 


0< 


TO  LINE 


FIG.  3456. — Polarized  Relay  (Siemens's  Pattern). 


strengthen  n  and  weaken  n',  the  tongue  will  be  attracted 
over  and  will  make  contact  against  the  stop  which  is  in  con- 
nexion with  the  local  battery,  and  so  will  work  the  sounder. 
If  the  current  flows  in  the  opposite  sense,  so  as  to  weaken  n 
and  strengthen  n',  the  tongue  will  tend  to  move  the  other 
way  and  will  make  no  signal.  Even  when  there  is  no  cur- 
rent the  tongue  returns  back,  being  attracted  to  the  nearer 
pole-piece.  No  springs  are  necessary. 

The  sensitive  form  of  polarized  relay,  adopted  in  the 
British  Postal  Telegraphs,  is  shown  in  Fig.  345  c.  Here  the 
tongue  of  the  relay  is  fixed  on  a  vertical  spindle,  pivoted  in 
jewelled  holes,  which  has  two  short  iron  projections  upon  it. 
This  spindle  is  polarized  by  a  powerful  steel  magnet  of 
compact  shape.  The  two  projections  lie  between  a  pair  of 


584         ELECTRICITY   AND   MAGNETISM     [PT.  n.  585,  586 

upper  and  a  pair  of  lower  pole-pieces  upon  the  two  vertical 
iron  cores  of  the  electromagnets.   These  are  wound  with  coils 

of  exceedingly  fine  silk-covered 
wire.  The  connexions  are  indi- 
cated in  Fig.  343  a  where  the 
tongue  of  the  relay  is  shown  to 
make  circuit,  when  it  touches  the 
stop,  for  a  local  battery  and  the 
Morse  ink-writer  Whenever  a 
current  comes  in  the  right  direc- 
tion in  the  line  it  causes  the 
tongue  of  the  relay  to  close  the 
local  circuit,  and  causes  the  Morse 
FIG.  345c.  —  Polarized  Relay  to  record  either  a  dot  or  a  dash 

(British  P.  O.  Pattern).  ,,  .    .          ,, 

on  the  strip  of  paper. 

585.  Faults  in  Telegraph  Lines.  —  Faults  may  occur  in 
telegraph  lines  from  several  causes ;    either  from  the  break- 
age of  the  wires  or  conductors,  or  from  the  breakage  of  the 
insulators,  thereby  short-circuiting  the  current  through  the 
earth  before  it  reaches  the  distant  station,  or,  as  in  overhead 
wires,  by  two  conducting  wires  touching  one  another.     Vari- 
ous modes  for  testing  the  existence  and  position  of  faults  are 
known  to  telegraph  engineers;    they  depend  upon  accurate 
measurements  of  resistance  or  of  capacity.     Thus,  if  a  tele- 
graph cable  part  in  mid-ocean  it  is  possible  to  calculate  the 
distance  from  the  shore  end  to  the  broken  end  by  comparing 
the  resistance  that  the  cable  is  known  to  offer  per  mile  with 
the  resistance  offered   by  the  length  up   to  the  fault,  and 
dividing  the  latter  by  the  former. 

586.  Duplex    and    Quadruplex    Telegraphy.  —  To    send 
two  messages  through  one  wire,  one  from  each  end,  at  the 
same  time,  is  known  as   duplex  working.     There    are  two 
distinct  methods  of  arranging  apparatus  for  duplex  working. 
The  first  of  these,  known  as  the  differential  method,  involves 
the  use  of  instruments  wound  with  differential  coils,  and  is 
applicable  to  special  cases.     The  second  method  of  duplex 


CH.  xiv.  586]  DUPLEX   TELEGRAPHY  585 

working,  known  as  the  bridge  method,  is  capable  of  much  more 
general  application.  The  diagram  of  Fig.  346  will  explain 
the  general  principle.  The  first  requirement  in  duplex 
working  is  that  the  instrument  at  each  end  shall  only  move 
in  response  to  signals  from  the  other  end,  so  that  an  operator 
at  R  may  be  able  to  signal  to  the  distant  instrument  M' 
without  his  own  instrument  M  being  affected,  M  being  all 
the  while  in  circuit  and  able  to  receive  signals  from  the  dis- 
tant operator  at  R'.  To  accomplish  this  the  circuit  is  divided 
at  R  into  two  branches,  which  go,  by  A  and  B  respectively, 
the  one  to  the  line,  the  other  through  a  certain  resistance 
P  to  the  earth.  If  the  ratio  between  the  resistances  in  the 
arms  RA  and  RB  is  equal  to  the  ratio  of  the  resistances  of  the 
line  and  of  P,  then, 
by  the  principle  of 
Wheatstone's  Bridge, 
no  current  will  pass 
through  M.  So  M 
does  not  show  any 

Currents  Sent  from  R*    ^IG>  ^4^ — Bridge  Method  of  Duplex  Telegraphy. 

but  M'  will  show  them,  for  the  current  on  arriving  at  C 
will  divide  into  two  parts,  part  flowing  round  to  the  earth 
by  R',  the  other  part  flowing  through  M'  and  producing 
a  signal.  If,  while  this  is  going  on,  the  operator  at  the 
distant  R'  depresses  his  key  and  sends  an  equal  current  in 
the  opposite  direction,  the  flow  through  the  line  will  cease ; 
but  M  will  now  show  a  signal,  because,  although  no  current 
flows  through  the  line,  the  current  in  the  branch  RA  will  now 
flow  down  through  M,  as  if  it  had  come  from  the  distant 
R',  so,  whether  the  operator  at  R  be  signalling  or  not,  M  will 
respond  to  signals  sent  from  R.  In  duplexing  long  lines  and 
cables  condensers  are  employed  in  the  arms  RA  and  RB  of 
the  bridge ;  and  instead  of  a  mere  balancing  resistance  at  P 
and  Q  there  is  used  an  "  artificial  cable,"  a  combination  of 
condensers  and  resistances  to  imitate  the  electrical  properties 
of  the  actual  line  or  cable  between  the  stations. 


586 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  586 


The  Diplex  method  of  working  consists  in  sending  two 
messages  at  once  through  a  wire  in  the  same  direction.  To 
do  this  it  is  needful  to  employ  one  set  of  instruments  which 
works  only  with  currents  in  one  given  direction,  and  a  second 
set  which  works  only  when  the  current,  in  either  direction, 
exceeds  a  certain  strength.  The  method  involves  the  use  of 
polarized  relays,  which,  being  themselves  permanently  mag- 
netized, respond  therefore  only  to  currents  in  one  direction, 
and  of  set-up  non-polarized  relays  which  will  not  respond  to 
currents  below  a  certain  minimum.  Two  keys  are  used ; 
one  reversing  the  current  and  sending  it  in  either  positive 
or  negative  direction,  the  other  sending  current  always  in 
the  same  direction,  but  sometimes  weak,  sometimes  strong. 

One  key  controls  the  direction,  the 
other  the  strength  of  the  current. 

The  method  used  by  Edison  for 
transmitting  is  shown  in  Fig.  347. 
In  the  position  shown  the  battery  B 
has  its  terminals  at  N  and  P ;  the 
current  passing  from  B  through  K2 
to  the  spring  S,  and  thence  to  P. 
If  the  key  K'  is  worked,  the  cur- 
rents flow  into  or  out  of  the  line, 

fl — I — I  [ill  III  ill  I '    anc^  ^  a  P°larized  relay  is  inserted 

B  B'  at  the  distant  receiving  station,  it 

will  work  its  sounder  only  for  cur- 
rents in  one  direction,  as  sent  by  K', 
no  matter  whether  these  currents  are  strong  or  weak.  As 
shown  in  the  figure,  the  second  battery  B',  which  has  more 
cells  than  B,  is  on  open  circuit.  If,  however,  K2  be  depressed, 
the  spring  S  comes  into  contact  with  the  point  m  and  breaks 
contact  with  n,  so  that  now  the  entire  range  of  battery  is 
thrown  into  operation.  Whenever  K2  is  depressed,  there- 
fore, the  points  N  and  P  retain  their  polarity,  but  the  current 
is  of  three  or  four  times  its  original  strength.  All  contacts 
are  made  by  springs  properly  adjusted  so  that  K2  never 


K2 


FIG.  347.  —  Diplex  Telegraphy 
(Edison  Transmitter). 


CH.  xiv.  586]     QUADRUPLEX   TELEGRAPHY  587 

breaks  the  circuit  in  producing  the  change  of  strength  of 
current.  The  message  transmitted  by  K2  is  received  on  a 
non-polarized  relay,  the  tongue  of  which  is  controlled  by  a 
spring  so  adjusted  that  the  weak  currents  of  battery  B  will 
not  cause  the  electromagnets  to  pull  over  the  armature; 
but  when  K2  is  worked,  the  current  due  to  B  +  B'  easily 
pulls  the  armature  over. 

The  Quadruplex  method  of  working  combines  the  duplex 
and  the  diplex  methods.  On  one  and  the  same  line  are  used 
two  sets  of  receiving  instruments,  one  of  which  (worked 
by  a  polarized  relay)  works  only  when  the  direction  of  the 
current  is  changed,  the  other  of  which  (worked  by  a  non- 
polarized relay  adjusted  with  springs  to  move  only  with  a 
certain  minimum  force)  works  only  when  the  strength  of  the 
current  is  changed  and  is  independent  of  their  direction.  In 
quadruplex  working,  as  in  duplex  working,  there  are  two  gen- 
eral methods  :  differential  methods,  depending  upon  the  bal- 
ancing of  currents  in  two  sets  of  windings ;  and  bridge 
methods,  depending  upon  the  balancing  of  potentials  as  in  a 
Wheatstone's  bridge.  If  in  Fig.  346,  —  which  is  a  bridge 
method,  —  the  diplex  transmitting  apparatus  just  described 
were  inserted  at  each  end  instead  of  the  two  keys  R  and  R', 
and  if  between  A  and  B  were  placed  in  series  the  two  relays, 
the  figure  would  represent  the  general  arrangement  of  the 
quadruplex  system  as  used  widely  in  the  United  States. 
The  differential  method,  as  distinguished  from  the  bridge 
method  of  duplexing,  is  also  commonly  used  in  quadruplex 
telegraphy,  expecially  on  land-lines  not  exceeding  300  miles 
in  length. 

The  two  methods  of  quadruplex  working  will  be  readily 
understood  by  reference  to  Figs.  348a  and  3486.  Fig.  348a 
shows  the  arrangement  of  the  apparatus  at  one  end  of  the 
line  for  quadruplexing  according  to  the  bridge  method. 
There  are  two  transmitters  Ti  and  T2  and  two  receiving 
relays  RI  and  R2,  both  the  latter  being  included  in  the  bridge 
circuit  corresponding  to  the  position  of  the  receiving  instru- 


588 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  586 


ment  M  in  Fig.  346.  A  similar  set  of  transmitting  and  re- 
ceiving instruments  are  similarly  grouped  at  the  other  end  of 
the  line.  The  transmitter  TI  reverses  the  direction  of  the 
current  of  the  battery  BI  without  altering  its  strength.  The 
transmitter  T2  throws  in  the  augmenting  battery  B2  to  alter 
the  strength  of  the  current  without  changing  its  direction. 


LINE 


FIG.  348o.  —  Bridge  Method  of  Quadruple  Telegraphy. 

It  therefore  corresponds  in  its  action  to  K2  in  Fig.  347,  but 
instead  of  being  worked  by  hand  it  is  worked  by  an  electro- 
magnet in  circuit  with  a  small  battery  62  and  operated  by  the 
key  K2.  It  is  found  that  the  electromagnet  works  the  lever 
of  T2  with  greater  sharpness  and  precision  than  can  be  at- 
tained by  hand  with  a  key  like  K2,  and  is  not  so  fatiguing  to 


CH.  xiv.  586]      QUADRUPLEX   TELEGRAPHY  589 

the  operator.  So  long  as  the  lever  of  T2  is  in  the  position 
shown  in  the  figure,  the  battery  BI  only  is  in  circuit;  but 
when  the  lever  is  depressed  the  small  spring  s  connects  wire 
w  to  the  positive  pole  of  the  battery  B2,  thereby  causing  a 
current  of  four-fold  strength  to  flow  to  the  line.  The  instru- 
ment TI  is  a  pole-changer  corresponding  to  KI  in  Fig.  347, 
and  merely  reverses  the  direction  of  the  current  in  the  line. 
The  receiving  instruments  which  are  situated  in  the  bridge 
are  unaffected  by  the  working  of  the  transmitters  KI  and  K2 
at  the  same  end  of  the  line,  but  respond  to  the  signals  sent 
from  the  distant  station  at  the  other  end.  The  receiving  instru- 
ment RI  is  a  polarized  relay  which  responds  only  to  currents 
in  the  positive  direction,  whatever  their  strength ;  it  therefore 
actuates  the  sounder  Si  only  when  the  key  KI  of  the  distant 
station  is  depressed.  The  other  receiving  instrument  R2  is 
a  non-polarized  (or  "  neutral  ")  relay,  the  lever  of  which  is 
held  back  by  an  adjustable  spring.  It  will  respond  to  cur- 
rents that  flow  in  either  the  positive  or  the  negative  direction, 
but  only  when  they  are  of  the  increased  strength  caused  by 
depressing  the  key  K2  at  the  distant  station.  It  may,  how- 
ever, happen  that  a  reversal  of  the  current  by  KI  occurs  in  the 
middle  of  a  signal  with  K2 ;  and  this,  if  it  occurred,  would 
cause  R2  to  let  slip  its  armature  for  a  fraction  of  a  second, 
producing  the  effect  of  a  double  signal  in  the  sounder  S2  if 
this  were  worked  directly  by  R2.  To  avoid  this  defect  an 
intermediate  relay  (an  up-righting  sounder)  S3  is  intro- 
duced in  a  local  circuit  of  its  own  between  R2  and  S2.  83 
operates  S2  by  contact  with  its  back  stop,  so  that  a  momentary 
release  of  the  lever  of  R2  does  not  affect  S2  unless  the  interval 
of  time  is  great  enough  for  the  lever  of  83  to  reach  its  back 
stop.  The  additional  magnet  m  in  series  with  the  condenser 
c  is  for  the  following  purpose.  While  R2  is  reversing,  the  con- 
denser discharges  itself  through  m  and  thus  holds  the  lever 
just  at  the  dead  point. 

When  the   differential  method  is  employed,   the  trans- 
mitting keys  may  be  arranged  as  in  Fig.  348  a  but  (in  lieu  of 


590 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  587 


the  bridge  arrangement)  after  the  circuit  divides  into  two  at 
the  point  y,  the  two  branches  are  wound  differentially  upon  the 
two  relays  Ri  and  R2  as  shown  in  Fig.  3486.  One  of  these 
branches  goes  to  the  line,  the  other  (shown  dotted)  goes  to 

earth  through  resistances  and  con- 
densers acting  as  an  artificial  line 
and  constructed  to  balance  the  re- 
sistance and  capacity  of  the  actual 
line.  Any  current  coming  from  the 
transmitters  in  the  home  station 
divides  into  two  equal  parts  which 
circulate  in  opposite  directions 
around  the  coils  of  the  relays,  and 
thus  produce  no  effect.  A  current 
from  the  distant  station  works  the 
polarized  relay  Ri  if  flowing  in  the 
positive  direction,  and  works  the 
non-polarized  set-up  relay  R2  if  of 
sufficient  strength.  The  conse- 
quences of  the  keys  at  both  ends  being  worked  at  the  same 
time  are  much  the  same  as  with  the  bridge  method ;  and 
can  easily  be  followed  out  by  the  student,  who  will  see  that 
there  are  16  different  possible  positions  of  the  keys,  in  all  of 
which  the  effect  upon  the  distant  station  receivers  is  exactly 
the  same  as  if  the  distant  station  keys  were  not  being 
worked ;  the  receiving  relays  at  one  end  answering  only  to 
signals  sent  from  the  other  end. 


FIG.  348  b.  —  Differential  Method 
of  Quadruples  Telegraphy. 


LESSON  LV.  —  Cable  Telegraphy 

587.  Submarine  Cables.  —  Telegraphic  communication 
between  two  countries  separated  by  a  strait  or  ocean  is  car- 
ried on  through  cables  sunk  to  the  bottom  of  the  sea,  which 
carry  conducting  wires  carefully  protected  by  an  outer  sheath 
of  insulating  and  protecting  materials.  The  conductor  is 
usually  of  purest  copper  wire,  weighing  from  70  to  400  Ibs.  per 


CH.  xiv.  588]  SUBMARINE    CABLES  591 

nautical  mile,  made  in  a  seven-fold  strand  to  lessen  risk  of 
breaking.  Figs.  349  a  and  349  6  show,  in  their  natural  size, 
sections  of  the  Atlantic  cables  laid  in  1857  and  1893  respec- 
tively. In  the  latter  cable,  which  is  of  the  usual  type  of  cable 
for  long  lines,  the  core  is  protected  first  by  a  stout  layer  of 


FIG.  349  a.  —  Section  of  1857  Atlantic         FIG.  349  b. — Section  of  1893  Atlantic 
Cable.  Cable. 

gutta-percha,  then  by  a  woven  coating  of  jute,  and  outside 
all  an  external  sheath  made  of  ten  iron  wires,  each  covered 
with  hemp.  The  shore  ends  are  even  more  strongly  pro- 
tected by  external  wires. 

588.  Speed  of  Signalling  through  Cables.  —  Signals  trans- 
mitted through  long  cables  are  retarded,  the  retardation 
being  due  to  two  causes. 

Firstj  The  self-induction  of  the  circuit  prevents  the  cur- 
rent from  rising  at  once  to  its  height,  the  retardation  being 
expressed  by  von  Helmholtz's  equation  (Art.  504). 

Secondly,  The  cable  in  its  insulating  sheath,  when  im- 
mersed in  water,  acts  laterally  like  a  Ley  den  jar  of  enormous 
capacity  (as  explained  in  Art.  321),  and  the  first  portions  of  the 
current,  instead  of  flowing  through,  remain  in  the  cable 
as  an  electrostatic  charge  on  the  surface  of  the  gutta-percha. 
For  every  separate  signal  the  cable  must  be  at  least  partially 
charged  and  then  discharged.  Culley  states  that  when  a 
current  is  sent  through  an  Atlantic  cable  from  Ireland  to  New- 
foundland no  effect  is  produced  on  the  most  delicate  instru- 
ment at  the  receiving  end  for  two-tenths  of  a  second,  and  that 
it  requires  three  seconds  for  the  current  to  gain  its  full 


592 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  588 


strength,  rising  in  an  electric  wave  which  travels  forward 
through  the  cable.  The  strength  of  the  current  falls  grad- 
ually also  when  the  circuit  is  broken.  The  greater  part  of 
this  retardation  is  due  to  electrostatic  charge,  not  to  elec- 
tromagnetic self-induction.  The  time  required  to  transmit 
a  given  number  of  signals  varies  in  proportion  both  to  K  the 
capacity  and  R  the  resistance  of  the  cable:  it  is  therefore 
proportional  to  KR,  and  as  each  of  these  quantities  is  propor- 
tional to  the  length  of  the  cable,  it  follows  that  the  retarda- 
tion is  proportional  to  the  square  of  the  length  of  the  cable. 


10 


7 


Receivec 


02          4         6         8         10        12      Time     16 

FIG.  350.  —  Curves  of  Transmission  and  Arrival. 

The  "  curve  of  arrival "  may  be  contrasted  with  the  shaded 
"curve  of  transmission"  (Fig.  350).  The  various  means 
adopted  to  get  rid  of  this  retardation  are  explained  in  Art. 
322.  It  is  usual  to  insert  in  the  circuit  at  each  end  of 
the  cable  a  condenser  of  several  microfarads,  through  which 
the  signals  pass.  The  tendency  of  the  condenser  to  dis- 
charge helps  to  curb  the  signals  and  make  each  shorter 
and  sharper.  It  is  theoretically  possible  (compare  Art. 
458)  to  compensate  capacity  by  self-induction;  but  as 
the  capacity  of  a  cable  is  lateral,  not  longitudinal,  and  dis- 
tributed all  along  it,  the  self-induction  coils  to  compensate 
the  retardation  would  have  to  be  applied  as  shunts  at  inter- 


CH.  xiv.  589]          RECEIVERS  FOR   CABLES 


593 


vals.  A  cable  with  a  self -inductive  shunt  or  leak  at  a  point 
near  its  middle  transmits  signals  more  rapidly  than  one  not 
so  compensated. 

589.  Receiving  Instruments  for  Cables.  —  The  mirror- 
galvanometer  of  Lord  Kelvin  (Art.  228)  was  devised  for  cable 
signalling,  the  movements  of  the  spot  of  light  sweeping  over 
the  scale  to  a  short  or  a  long  distance,  sufficing  to  signal  the 


Fia.  351.  —Kelvin's  Siphon  Recorder. 

dots  and  dashes  of  the  Morse  code.  Lord  Kelvin's  Siphon 
Recorder  (Fig.  351)  is  an  instrument  which  writes  the 
signals  upon  a  strip  of  paper  by  the  following  ingenious 
means  :  —  The  cable  communicates  with  a  delicately-sus- 
pended coil  of  wire  that  hangs  between  the  poles  of  a 
powerful  magnet.  To  the  suspended  coil  is  attached  a  fine 
siphon  of  glass  suspended  by  a  silk  fibre,  one  end  of  which 
dips  into  an  ink  vessel.  The  ink  makes  marks  upon  a 
2Q 


594         ELECTRICITY   AND   MAGNETISM   [PT.  n.  590,  591 

strip  of  paper  (moved  by  clockwork  vertically  past  the 
siphon),  friction  being  obviated  by  giving  the  siphon  a 
continual  minute  vibration.  The  siphon  record  is  a  wavy 
line  having  little  bends  above  or  below  the  central  line  of 
the  strip  for  dots  or  dashes. 


LESSON  LVI.  —  Miscellaneous  Telegraphs 

590.  Multiplex   Telegraphs.  —  Varley  proposed  to  send 
messages  by  transmitting  electrically  musical  tones,  inter- 
rupted to  sound  as  dots  and  dashes.     This  necessitated  the 
transmission  of  currents  either  rapidly  alternating  or  rapidly 
intermittent.     Gray,  who   constructed   harmonic  telegraphs 
on   this   plan,  found   it   possible   to   transmit   five   or   six 
messages  simultaneously  in  one  line. 

By  using  at  each  end  of  a  line  two  synchronously  revolving 
distributing  switches,  it  is  possible  to  send  several  messages 
at  once  through  a  line ;  the  distributors  (invented  by  Delany) 
causing  each  transmitting  instrument  to  be  in  circuit  with  its 
corresponding  receiving  instrument  for  a  small  fraction  of  a 
second  at  regular  short  intervals. 

591.  Electric    Bells.  —  The    common    form    of    Electric 
Trembling  Bell  (invented  1850  'by  John  Mirand)   consists 
of  an   electromagnet,   which   moves  a  hammer  backward 
and  forward  by  alternately  attracting  and  releasing  it,  so 
that  it  beats  against  a  bell.     The  arrangements  of  the  in- 
strument are  shown  in  Fig.  352  a,  in  which  E  is  the  electro- 
magnet and  H  the  hammer.     A  battery,  consisting  of  one  or 
two  Leclanche  cells  placed  at  some  convenient  point  of  the 
circuit,  provides  a  current  when  required.     By  touching  the 
"  push  "  P,  the  circuit  is  completed,  and  a  current  flows 
along  the  line  and  round  the  coils  of  the  electromagnet,  which 
forthwith  attracts  a  small  piece  of  soft  iron  attached  to  the 
lever,  which  terminates  in  the  hammer  H.     The  lever  is  itself 
included  in  the  circuit,  the  current  entering  it  above  and 
quitting  it  at  C  by  a  contact-breaker,  consisting  of  a  spring 


CH.  xiv.  591] 


ELECTRIC  BELLS 


595 


tipped  with  platinum  resting  against  the  platinum  tip  of  a 
screw,  from  which  a  return  wire  passes  back  to  the  zinc  pole 
of  the  battery.  As  soon  as  the  lever  is  attracted  forward  the 
circuit  is  broken  at  C  by  the  spring  moving  away  from  con- 
tact with  the  screw ;  hence  the  current  stops,  and  the  electro- 
magnet ceases  to  attract  the  armature,  but  the  momentum  of 
the  hammer  carries  it  forward.  Immediately  afterwards, 
however,  the  hammer  falls  back,  again  establishing  con- 
tact at  C,  whereupon  the  armature  is  once  more  attracted 
forward,  and  so  on.  The  push  P  is  shown  in  section  in 


FIG.  352  a.  —  Electric  Trembling  Bell. 


FIG.  352  b. 


Fig.  352  6.  It  usually  consists  of  a  cylindrical  knob  of 
ivory  or  porcelain  capable  of  moving  loosely  through  a  hole 
in  a  circular  support  of  porcelain  or  wood,  and  which,  when 
pressed,  forces  a  platinum-tipped  spring  against  a  metal  pin, 
and  so  makes  electrical  contact  between  the  two  parts  of  the 
interrupted  circuit.  Bells,  having  a  polarized  armature,  and 
without  any  break,  are  used  as  call-bells  or  telephones ;  the 
generator  being  a  small  magneto  alternator  like  Fig.  285, 
driven  by  a  handle. 


596  ELECTRICITY  AND   MAGNETISM      [PT.  n.  592 

592.  Electric  Clocks  and  Chronographs.  —  Clocks  may  be 
either  driven  or  controlled  by  electric  currents.  Bain, 
Hipp,  and  others  devised  electric  clocks  of  the  first  kind,  in 
which  the  ordinary  motive-power  of  a  weight  or  spring  is 
abandoned,  the  clock  being  driven  by  its  pendulum,  the 
"  bob  "  of  which  is  an  electromagnet  alternately  attracted 
from  side  to  side.  The  difficulty  of  maintaining  a  perfectly 
constant  battery  current  delayed  progress.  Hope- Jones 
overcame  this  difficulty  by  causing  »the  current,  acting 
through  an  electromagnet,  to  lift  a  small  weight,  which  in 
descending  drives  the  mechanism  of  the  clock  with  an  un- 
varying force. 

Electrically  controlled  clocks,  governed  by  a  standard 
central  clock,  have  proved  a  fruitful  invention.  In  these 
the  standard  timekeeper  is  constructed  so  as  to  complete  a 
circuit  periodically,  once  every  minute  or  half  minute.  The 
transmitted  currents  set  in  movement  the  hands  of  a  system 
of  dials  placed  at  distant  points,  by  causing  an  electromagnet 
placed  behind  each  dial  to  attract  an  armature,  which,  acting 
upon  a  ratchet  wheel  by  a  pawl,  causes  it  to  move  forward 
through  one  tooth  at  each  specified  interval,  and  so  carries 
the  hands  round  at  the  same  rate  as  those  of  the  standard 
clock. 

Electric  chronographs  are  used  for  measuring  very  small 
intervals  of  time.  A  stylus  fixed  to  the  armature  of  a  small 
electromagnet  traces  a  line  upon  a  piece  of  paper  fixed  to  a 
cylinder  revolving  by  clockwork.  A  current  sent  through 
the  coils  of  the  electromagnet  moves  the  armature  and  causes 
a  lateral  notch  in  the  line  so  traced.  A  second  current  marks 
a  second  notch ;  and  from  the  interval  of  space  between  the 
two  notches  the  interval  of  time  which  elapsed  between  the 
two  currents  may  be  calculated  to  the  ten-thousandth  part 
of  a  second  if  the  speed  of  rotation  is  accurately  known. 
The  velocity  with  which  a  cannon  ball  moves  along  the  bore 
of  the  cannon  can  be  measured  thus. 


CH.  xiv.  593]  TELEPHONES  597 

LESSON  LVII.  —  Electric  Telephones 

593.  Early  Telephones.  —  The  first  successful  attempt  to 
transmit  sounds  electrically  was  made  in  1861  by  Reis,  who 
succeeded  in  conveying  musical  and  other  tones  by  an  imper- 
fect telephone.  In  this  instrument  the  voice  was  caused  to 
act  upon  a  point  of  loose  contact  in  an  electric  circuit,  and  by 
bringing  those  parts  into  greater  or  less  intimacy  of  contact 
(Art.  432),  thereby  varied  the  resistance  offered  to  the 
circuit.  The  transmitting  part  of  Reis's  telephone  consisted 
of  a  battery  and  a  contact-breaker,  the  latter  being  formed  of 
a  tympanum  or  diaphragm  of  stretched  membrane,  capable 
of  taking  up  sonorous  vibrations,  and  having  attached  to 
it  a  thin  elastic  strip  of  platinum,  which,  as  it  vibrated, 
beat  to  and  fro  against  the  tip  of  a  platinum  wire,  so  making 
and  breaking  contact  wholly  or  partially  at  each  vibration 
in  exactly  the  same  manner  as  is  done  with  the  carbon  con- 
tacts in  the  modern  transmitters  of  Blake,  Berliner,  etc. 
The  receiving  part  of  the  instrument  consisted  of  an  iron 
wire  fixed  upon  a  sounding-board  and  surrounded  by  a  coil 
of  insulated  wire  forming  part  of  the  circuit.  The  rapid 
magnetization  and  demagnetization  of  such  an  iron  core 
will  produce  audible  sounds  (Art.  125).  If  the  current  vary, 
the  iron  wire  is  partially  magnetized  or  demagnetized,  giving 
rise  to  corresponding  vibrations  of  varying  amplitudes  and 
forms ;  hence  such  a  wire  will  serve  perfectly  as  a  receiver 
to  reproduce  speech  if  a  good  transmitter  is  used.  Reis 
himself  transmitted  speech  with  his  instrument,  but  only  im- 
perfectly, for  all  tones  of  speech  cannot  be  transmitted  by 
abrupt  interruptions  of  the  current,  to  which  Reis's  trans- 
mitter is  prone  when  spoken  into,  owing  to  the  extreme 
lightness  of  the  contact :  they  require  gentle  undulations, 
sometimes  simple,  sometimes  complex,  according  to  the 
nature  of  the  sound.  The  vowel  sounds  are  produced 
by  periodic  and  complex  movements  in  the  air;  the  con- 
sonants being  for  the  most  part  non-periodic.  Reis  also 


598  ELECTRICITY  AND   MAGNETISM     [FT.  n.  593 

devised  a  second  receiver,  in  which  an  electromagnet 
attracted  an  elastically-supported  armature  of  iron,  which 
vibrated  under  the  attraction  of  the  more  or  less  interrupted 
current. 

In  1876  Elisha  Gray  devised  a  transmitter  in  which  a 
variable  water-resistance  (made  by  a  platinum  wire  dipping 
into  water)  was  acted  upon  by  the  voice.  He  designed  an 
electromagnetic  receiver. 

Telephone  receivers  were  invented  by  Varley  and  Dolbear, 
in  which  the  attraction  between  the  oppositely-electrified 
armatures  of  a  condenser  is  utilized  in  the  production  of 
sounds.  Dolbear's  receiver  consists  merely  of  two  thin 
metal  disks,  separated  by  a  very  thin  air-space.  As  the  vary- 
ing currents  flow  into  and  out  of  this  condenser  the  two 
disks  attract  one  another  more  or  less  strongly,  and  thereby 
vibrations  are  set  up  which  correspond  to  the  vibrations  of 
the  original  sound. 

In  1876  Graham  Bell  invented  the  magneto-telephone. 
In  this  instrument  the  speaker  talks  to  an  elastic  plate  of 
thin  sheet  iron,  which  vibrates  and  transmits 
its  every  movement  electrically  to  a  similar 
plate  in  a  similar  telephone  at  a  distant  sta- 
tion, causing  it  to  vibrate  in  an  identical 
manner,  and  thereby  to  emit  identical  sounds. 
The  transmission  of  the  vibrations  depends 
upon  the  principles  of  magneto-electric  induc- 
tion explained  in  Lesson  XVIII.  Fig.  352  c 
shows  Bell's  Telephone  in  section.  The  disk 
D  is  placed  behind  a  conical  mouthpiece,  to 
FIG.  352  c.— Bell's  which  the  speaker  places  his  mouth  or  the 
hearer  his  ear.  Behind  the  disk  is  a  magnet 
AA  running  the  length  of  the  instrument;  and  upon  its 
front  pole,  which  nearly  touches  the  disk,  is  fixed  a  small 
bobbin,  on  which  is  wound  a  coil  C  of  fine  insulated  wire, 
the  ends  of  the  coil  being  connected  with  the  terminal 
screws  FF.  One  such  instrument  is  used  to  transmit, 


CH.  xiv.  594]      TELEPHONE    TRANSMITTERS  599 

and  one  to  receive  the  sounds,  the  two  being  connected  in 
simple  circuit.  No  battery  is  needed,  for  the  transmitting 
instrument  itself  generates  the  induced  currents  as  follows : 
The  magnet  AA  induces  a  certain  number  of  magnetic  lines 
through  the  coil  C.  Many  of  these  pass  into  the  iron  disk. 
When  the  iron  disk  in  vibrating  moves  toward  the  magnet 
pole,  more  magnetic  lines  meet  it;  when  it  recedes,  fewer 
lines  meet  it.  Its  motion  to  and  fro  will  therefore  alter  the 
number  of  lines  which  pass  through  the  hollow  of  the  coil  C,  and 
will  therefore  (Art.  243)  generate  in  the  wire  of  the  coils  cur- 
rents whose  strength  is  proportional  to  the  rate  of  change  in 
the  number  of  the  lines.  Bell's  instrument,  when  used  as  a 
transmitter,  may  therefore  be  regarded  as  a  sort  of  vibrating 
dynamo,  which  pumps  currents  in  alternate  directions  into 
the  wire.  At  the  distant  end  the  currents  as  they  arrive  flow 
round  the  coils  either  in  one  direction  or  the  other,  and  there- 
fore either  add  momentarily  to  or  take  from  the  strength  of 
the  magnet.  When  the  current  in  the  coils  is  in  such  a  direc- 
tion as  to  reinforce  the  magnet,  the  magnet  attracts  the  iron 
disk  in  front  of  it  more  strongly  than  before.  If  the  current  is 
in  the  opposite  direction,  the  disk  is  less  attracted  and  flies 
back.  Hence,  whatever  movement  is  imparted  to  the  disk 
of  the  transmitting  telephone,  the  disk  of  the  distant  receiving 
telephone  is  forced  to  repeat,  and  it  therefore  throws  the  air 
into  similar  vibrations,  and  so  reproduces  the  sound.  Bell's 
method  of  transmitting  was  soon  abandoned  (except  for  very 
short  lines).  In  modern  telephonic  work  Reis's  plan  of  using 
a  separate  transmitter  with  a  battery  is  universal,  the  Bell 
instrument  being  used  as  a  receiver  only  and  not  as  a  trans- 
mitter. 

594.  Edison's  Transmitter.  —  Edison  constructed  a  trans- 
mitting instrument,  in  which  the  vibrations  of  the  voice, 
actuating  a  diaphragm  of  mica,  made  it  exert  more  or  less  com- 
pression on  a  button  of  prepared  lamp-black  placed  in  the 
circuit.  The  resistance  of  this  is  affected  by  pressure  of 
contacts ;  hence  the  varying  pressures  due  to  the  vibrations 


600  ELECTRICITY  AND   MAGNETISM     [PT.  n.  595 

cause  the  button  to  offer  a  varying  resistance  to  any  current 
flowing  (from  a  battery)  in  the  circuit,  and  vary  its  strength 
accordingly.  This  varying  current  may  be  received  as  be- 
fore in  an  electromagnetic  receiver  of  the  type  described 
above,  and  there  set  up  corresponding  vibrations.  This 
instrument  also  has  been  abandoned  in  favour  of  transmitters 
of  the  microphone  type.  Edison  also  invented  a  receiver 
of  singular  power,  which  depends  upon  a  curious  fact  dis- 
covered by  himself,  namely,  that  if  a  platinum  point  presses 
against  a  rotating  cylinder  of  moist  chalk,  the  friction  is  re- 
duced when  a  current  passes  between  the  two.  And  if  the 
point  be  attached  to  an  elastic  disk,  the  latter  is  thrown  into 
vibrations  corresponding  to  the  fluctuating  currents  coming 
from  the  speaker's  transmitting  instrument. 

595.    Microphones.  —  Hughes,   in   1878,    discovered  that 
a  loose  contact  between  two  conductors,  forming  part  of  a  cir- 


FIG.  353.  —  Hughes'  Microphone. 


cuit  in  which  a  small  battery  and  a  receiving  telephone  are 
included,  may  serve  to  transmit  sounds  without  the  inter- 
vention of  any  specific  tympanum  or  diaphragm  like  those  of 
Reis  and  Edison,  because  the  smallest  vibrations  will  affect 


CH.  xiv.  595]    MICROPHONIC   TRANSMITTERS  601 

the  resistance  (Art.  432)  at  the  point  of  loose  contact.  The 
Microphone  (Fig.  353)  embodies  this  principle.  In  the  form 
shown  in  the  figure,  a  small  thin  pencil  of  carbon  is  supported 
loosely  between  two  little  blocks  of  the  same  substance  fixed 
to  a  sounding-board  of  thin  pine-wood,  the  blocks  being  con- 
nected with  one  or  two  small  cells  and  a  Bell  receiver.  The 
amplitude  of  the  vibrations  emitted  by  the  receiver  may  be 
much  greater  than  those  of  the  original  sounds,  and  therefore 
the  microphone  may  serve,  as  its  name  indicates,  to  magnify 
minute  sounds,  such  as  the  ticking  of  a  watch  or  the  footfalls 
of  an  insect,  and  render  them  audible.  In 
modern  telephony  microphones  under 
the  name  of  carbon  transmitters  are  in 
general  use.  In  the  Blake  transmitter 
a  pin  of  platinum  is  pressed  by  a  light 
spring  against  a  polished  plug  of  hard  car- 
bon, forming  a  delicate  contact  through 
which  the  current  flows.  This  electrical 
mechanism  is  mounted  behind  a  metal 

,.   ,  ,  ,  .,          .  .       ,          FIG.  354.  —  Hunnings's 

dlSK     tO     take     Up     trie     Vibrations     Ol     tne  Microphonic  Transmitter. 

speaker's  voice.  In  the  Runnings  loud- 
speaking  transmitter  granulated  coke  carbon  is  placed  loosely 
between  two  metal  or  carbon  surfaces  EE,  so  that  the  numer- 
ous contacts  will  carry  a  stronger  current.  Fig.  354  gives 
a  section  of  this  transmitter,  in  which  M  is  the  mouthpiece, 
EE  the  carbon  electrodes  between  which  are  the  carbon 
granules,  and  D  the  diaphragm  which  responds  to  the  vibra- 
tions of  the  voice  communicated  to  the  mouthpiece  M,  thus 
causing  a  variation  of  the  resistance  through  the  granules 
and  a  corresponding  variation  in  the  current  transmitted  to 
the  line. 

For  all  long-line  work  the  microphone  transmitter  is 
included  with  a  battery  of  one  or  two  cells  in  a  small  local 
circuit  of  low  resistance,  in  which  is  inserted  the  primary 
wire  of  a  small  transformer  or  induction  coil.  The  secondary 
wire  of  this  transformer  is  a  coil  of  fine  wire  of  many  turns, 


602         ELECTRICITY  AND   MAGNETISM    [PT.  n.  596,  597 

which  transmits  through  the  line  and  return  circuits  smaller 
currents  at  a  higher  voltage. 

596.  Telephone  Exchanges.  —  For  enabling  a  large  num- 
ber of  subscribers  to  communicate  by  telephone  with  one 
another,  the  lines  from   each   subscriber's   instrument   are 
brought  to  a  central  office  known  as  a  telephone  exchange. 
Here  each   line  terminates   on   a   switch-board  which   is  so 
arranged  that  the  operator  can  in  an  instant  make  a  con- 
nexion from  the  line  of  any  one  subscriber  to  that  of  any 
other,  so  that  these  two  can  talk  together. 

597.  Hughes'   Induction  Balance.  —  The  extreme  sensi- 
tiveness of  Bell's  receiver  (Art.  593)  to  the  feeblest  currents 


FIG.  355.  —  Hughes'  Induction  Balance. 

has  suggested  its  employment  to  detect  currents  too  weak 
to  affect  most  delicate  galvanometers.  The  currents  must 
be  intermittent,  or  alternating,  or  they  will  not  keep  the 
disk  of  the  telephone  in  vibration.  Hughes  applied  this 
property  of  the  telephone  to  an  instrument  named  the  In- 
duction Balance  (Fig.  355).  A  small  battery  B,  connected 
with  a  microphone  M,  passes  through  two  coils  of  wire  PI,  Pz, 
wound  on  bobbins  fixed  on  a  suitable  stand.  Above  each 
of  these  primary  coils  are  placed  two  secondary  coils,  Si,  S2, 
of  wire,  of  the  same  size,  and  of  exactly  equal  numbers  of 
turns  of  wire.  The  secondary  coils  are  joined  to  a  receiver  T, 
and  are  wound  in  opposite  directions.  The  result  of  this  ar- 
rangement is  that  whenever  a  current  either  begins  or  stops 


CH.  xiv.  598, 599]     THE    TELEGRAPHONE  603 

flowing  in  the  primary  coils,  Pi  induces  a  current  in  Si,  and 
P2  in  S2. 

As  Si  and  S2  are  wound  in  opposite  ways,  the  two  currents 
thus  induced  in  the  secondary  wire  neutralize  one  another, 
and,  if  they  are  of  equal  strength,  balance  one  another  so 
exactly  that  no  sound  is  heard  in  the  telephone.  But  a 
perfect  balance  cannot  be  obtained  unless  the  resistances 
and  the  coefficients  of  mutual  induction  and  of  self-induction 
are  alike.  If  a  flat  piece  of  silver  or  copper  (such  as  a  coin) 
be  introduced  between  Si  and  Pi,  there  will  be  less  induction 
in  Si  than  in  S2,  for  part  of  the  inductive  action  in  PI  is  now 
spent  on  setting  up  currents  in  the  mass  of  the  metal  (Art. 
500),  and  a  sound  will  again  be  heard  in  the  telephone.  But 
balance  can  be  restored  by  moving  S2  farther  away  from  P2, 
until  the  induction  in  S2  is  reduced  to  equality  with  Si,  when 
the  sounds  in  the  telephone  again  cease.  It  is  possible  by 
this  means  to  test  the  relative  conductivity  of  different  metals 
which  are  introduced  into  the  coils.  It  is  even  possible  to 
detect  a  counterfeit  coin  by  the  indication  thus  afforded  of 
its  conductivity.  The  induction  balance  has  also  been 
applied  in  surgery  by  Graham  Bell  to  detect  the  presence  of 
a  bullet  in  a  wound,  for  a  lump  of  metal  may  disturb  the  in- 
duction when  some  inches  distant  from  the  coils. 

598.  Brown's  Relay.  —  Recently  a  form  of  relay  has  been 
devised  by  S.  G.  Brown  which  enables  telephonic  speech 
to  be  relayed  from  one  circuit  to  another  with  a  considerable 
augmentation  of  loudness.     The  relay  is  constructed  with  a 
carefully  balanced  lever  and  with  working  parts  made  of 
"  invar "   steel  which  does  not  expand  or  contract  with 
changes  of  temperature. 

599.  The  Telegraphone.  —  Poulsen  has  contrived  an  in- 
strument capable  of  recording  and  reproducing  telephonic 
speech.     In  the  telephone  circuit  is  included  a  minute  elec- 
tromagnet which  records  magnetically  the  variations  of  cur- 
rent upon  a  wire  (or  plate)  of  tungsten  steel  which  runs  be- 
neath its  poles.     The  series  of  minute  poles  thus  imprinted 


604  ELECTRICITY  AND  MAGNETISM     [PT.  11.  599 

on  the  moving  steel  is  quite  invisible ;  but  when  this  magnetic 
record  is  afterwards  caused  to  run  under  the  poles  of  a  similar 
electromagnet  in  a  circuit  containing  a  telephone  receiver, 
the  listener  hears  the  speech  reproduced ;  the  apparatus  act- 
ing as  a  magnetic  kind  of  phonograph. 


CHAPTER  XV 

ELECTRIC   WAVES 

LESSON  LVIII.  —  Oscillations  and  Waves 

600.  Electric  Oscillations.  —  If  a  charged  condenser  or 
Ley  den  jar  is  discharged  slowly  through  a  conductor  of 
high  resistance,  such  as  a  nearly  dry  linen  thread,  the  charge 
simply  dies  away  by  a  discharge  which  increases  in  strength 
at  first  and  then  gradually  dies  away.  If,  however,  the  con- 
denser is  discharged  through  a  coil  of  wire  of  one  or  more 
turns  (the  spark  being  taken  between  polished  knobs  to  pre- 
vent premature  partial  discharges  by  winds  or  brushes), 
the  effect  is  wholly  different,  for  then  the  discharge  consists 
of  a  number  of  excessively  rapid  oscillations  or  surgings. 
The  snapping  sound  of  an  oscillating  spark  is  very  distinc- 
tive. Oscillations  arise  because  of  the  self-inductance  of 
the  circuit,  by  reason  of  which  (Art.  501)  the  current  once 
set  up  tends  to  go  on.  The  first  rush  more  than  empties  the 
condenser,  and  charges  it  the  opposite  way ;  then  follows  a 
reverse  rush,  which  also  overdoes  the  discharge  and  charges 
the  condenser  the  same  way  as  at  first,  and  so  forth.  Each 
successive  oscillation  is  feebler  than  the  preceding,  so  that 
after  a  number  of  oscillations  the  discharge  dies  away  as  in 
Fig.  356.  This  effect,  whether  due  to  the  waste  of  energy 
by  resistance  in  the  path,  or  to  energy  being  radiated  away 
in  waves,  is  called  damping.  If  there  were  no  loss  of  energy 
by  resistance  or  radiation  there  would  be  a  long  series  of  un- 
damped oscillations,  that  is  with  practically  no  decrement  in 
the  amplitudes  of  successive  oscillations.  The  spark  of  a 
jar  discharged  through  a  circuit  of  low  resistance  really 
consists  of  a  number  of  successive  sparks  in  reverse  direc- 

605 


606 


ELECTRICITY  AND   MAGNETISM     [PT.  n.  600 


tions.  One  proof  of  this,  as  pointed  out  by  Henry  in  1842 
from  the  experiments  of  Savery,  is  that  if  jar  discharges 
through  a  coil  are  used  to  magnetize  steel  needles,  the  direc- 
tion of  the  magnetization  is  anomalous,  being  sometimes  one 

way,  sometimes  the  other.  Fig. 
357  shows  two  forms  of  oscillating 
circuits,  as  used  by  Sir  Oliver  Lodge 
in  his  investigations.  In  any  such 
circuit  the  three  essentials  are : 
(i.)  capacity,  (ii.)  self-inductance, 
(iii.)  a  spark-gap.  Also,  the  resist- 
ance must  be  small. 

That  a  discharge  under  certain  conditions  will  be  oscilla- 
tory was  noted  by  von  Helmholtz.  Lord  Kelvin  in  1853 
predicted  these  conditions.  If  the  capacity  of  the  condenser 


FIG.  356.  —  Diagram   of  Electric 
Oscillations. 


FIG.  357.  —  Arrangements  of  Oscillatory  Circuits  (Lodge). 

is  C  (farads),  the  resistance  of  the  circuit  R  (ohms),  and  its 
inductance  L  (henries),  there  will  be  oscillations  if 

R<  V4L/C; 

and  there  will  be  no  oscillations  if 
R  >  V 


In  the  former  case  the  frequency  n  of  the  oscillations  will 
be  such  that 

L  - 


=         - 


Example.  —  If    C  =  0*01    microfarad,    L  =  O'OOOOl    henry,    and 
R  =  O,  n  =  503,000. 


CH.  xv.  601]  ELECTRIC    WAVES  607 

If  R  is  small,  n  is  nearly  equal  to  1  -r-  2  TT  VOL. 

The  oscillations  can  be  made  slower  by  increasing  either 
C  or  L.  The  oscillations  of  an  ordinary  Ley  den  jar  dis- 
charge may  last  only  from  a  ten-thousandth  to  a  ten-mil- 
lionth of  a  second.  By  using  coils  of  well-insulated  wire  and 
large  condensers,  Lodge  succeeded  in  slowing  down  the 
oscillations  to  400  a  second  ;  the  spark  then  emitting  a  musi- 
cal note.  Iron  is  found  to  retain  its  magnetic  properties 
even  for  oscillations  of  the  frequency  of  one  million  per 
second. 

Feddersen  in  1859  examined  the  spark  of  a  Ley  den  jar  by 
means  of  a  rotating  mirror,  and  found  that  instead  of  being 
a  single  instantaneous  discharge,  it  exhibited  definite  fluctua- 
tions.1 With  very  small  resistances  in  the  circuit,  there 
was  a  true  oscillation  of  electricity  backward  and  forward 
for  a  brief  time.  The  period  of  the  oscillations  was  found 
to  be  proportional  to  the  square  root  of  the  capacity  of  the 
condenser.  With  a  certain  higher  resistance  the  discharge 
became  continuous  but  not  instantaneous.  With  a  still 
higher  resistance  the  discharge  consisted  of  a  series  of  partial 
intermittent  discharges,  following  one  another  in  the  same 
direction.  Such  sparks  when  viewed  in  the  rotating  mirror 
showed  a  series  of  separate  images  at  nearly  equal  distances 
apart. 

601.  Electric  Waves.  —  Though  the  increasing  and  dying 
away  of  currents,  for  example  in  cables,  is  sometimes  loosely 
described  as  of  "  waves  "  of  current,  these  phenomena  are 
very  different  from  those  of  true  electric  or  electromagnetic 
waves  propagated  across  space.  In  the  case  of  true  electric 
waves,  portions  of  the  energy  of  the  current  or  discharge  are 
thrown  off  from  the  conductor  and  do  not  return  back  to  it, 
but  go  travelling  on  in  space.  If  a  current  increases  in 
strength  the  magnetic  field  around  it  also  increases,  the  mag- 
netic lines  enlarging  from  the  conductor  outward,  like  the 

1  These  electric  oscillations  were  examined  also  by  Schiller,  Overbeck, 
Blaserna,  and  others,  notably  by  Hertz ;  see  Art.  605  below. 


608  ELECTRICITY  AND   MAGNETISM      [FT.  n.  602 

ripples  on  a  pond.  But  as  the  current  is  decreased  the 
magnetic  lines  all  return  back  and  close  up  upon  the  conduc- 
tor ;  the  energy  of  the  magnetic  field  returns  back  into  the 
system.  But  if  for  currents  slowly  waxing  and  waning  we 
substitute  electric  oscillations  of  excessive  rapidity,  part 
of  their  energy  radiates  off  into  the  surrounding  medium  as 
electromagnetic  waves,  and  only  part  returns  back.  As  will 
be  presently  set  forth,  these  waves  possess  all  the  optical 
properties  of  light-waves,  and  can  be  reflected,  refracted, 
polarized,  etc.  Such  waves,  when  they  fall  upon  suitable 
conducting  circuits  can  in  turn  set  up  electric  oscillations 
therein,  the  wave-energy  being  absorbed  thereby  and  trans- 
formed into  the  energy  of  oscillating  currents. 

It  is  a  fundamental  part  of  the  modern  views  of  electric 
action  that  while  an  electric  displacement  (Art.  58)  is  being 
produced  in  a  dielectric,  the  effect  in  surrounding  space  is 
the  same  as  if  there  had  been  a  conductive  instead  of  an 
inductive  transfer  of  electricity.  Maxwell  gave  the  name 
of  displacement-current  to  the  rate  of  change  of  the  dis- 
placement. Experiment  proves  that  displacement-cur- 
rents, while  they  last,  set  up  magnetic  fields  around  them, 
just  as  convection-currents  (Art.  429)  and  conduction-currents 
do. 

602.  Resonating  Circuits.  Syntony.  —  The  circumstance 
that  when  certain  definite  relations  exist  between  the  capacity 
and  inductance  of  a  circuit  and  the  frequency  of  the  periodic 
currents,  the  choking  reactions  of  these  properties  neutralize 
one  another,  has  been  already  alluded  to  in  Art.  529.  And 
we  have  seen  (Art.  600)  that  a  circuit  with  a  certain  self- 
induction,  capacity,  and  resistance  tends  to  oscillate  elec- 
trically at  a  certain  frequency.  If  it  be  placed  in  a  medium 
through  which  electric  waves  of  that  frequency  are  passing 
in  such  a  position  that  the  electric  and  electromagnetic  fields 
of  the  successive  waves  can  induce  currents  in  it,  each  wave 
will  give  a  slight  impulse  to  the  readily-excited  oscillations, 
which  will  grow  in  intensity,  just  as  small  impulses  given  at  the 


CH.  xv.  603] 


ELECTRIC   RESONANCE 


609 


FIG.  358.  —  Electric  Oscillations  gradually  built 
up. 


right  times  to  a  pendulum  will  make  it  swing  violently.  Fig. 
358  illustrates  the  building-up  action  of  these  timed  impulses. 
The  following  experiment  of  Sir  Oliver  Lodge  beautifully 
illustrates  this  phenomenon  of  resonance,  or  syntony,  and  also 
illustrates  the  adjustment  by  tuning  of  an  oscillatory  circuit. 
Two  Ley  den  jars,  Fig. 
359,  are  placed  a  little 
way  apart  from  one  an- 
other. One  of  them, 
charged  from  an  in- 
fluence machine  (not 
shown),  is  provided  with 
a  bent  wire  to  serve  as 
a  discharging  circuit, 
with  a  spark-gap  S  between  the  polished  knobs  at  the  top. 
The  second  jar  is  provided  with  a  circuit  of  wire,  the  induc- 
tance of  which  can  be  adjusted  by  sliding  in  or  out  a  cross- 
piece  W  hooked  upon  the  other  portions.  A  strip  of  tinfoil 
is  brought  up  from  the  inner  coating  over  the  lip  of  this  jar, 

but  does  not  quite  touch  the  outer 
coating.  If  the  two  circuits  are 
properly  tuned  together,  whenever 
a  spark  passes  in  the  gap  at  the  top 
of  A,  surgings  will  be  set  up  in  the 
circuit  of  B  which  will  cause  the 
jar  to  overflow,  producing  a  spark 
at  the  end  of  the  strip.  The  pro- 
cess of  adjustment,  by  varying 
either  the  inductance  or  the  capacity  of  a  circuit,  so  as  to 
bring  it  into  syntony  with  another  circuit,  is  called  tuning. 
603.  High-Frequency  Apparatus.  —  Apparatus  for  gen- 
erating oscillatory  discharges  of  frequencies  that  may  attain 
millions  of  periods  per  second  have  been  devised  by  Elihu 
Thomson,  Nikola  Tesla,  and  others.  They  consist  in  gen- 
eral of  devices  for  sending,  by  means  of  induction  coils  (Art. 
246)  or  high-voltage  transformers  (Art.  538),  torrents  of 


FIG.  359.  —  Lodge's  Experiment 
on  Resonance. 


610 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  603 


blast 


FIG.  360.  —  Devices  for  Sudden  Extinction 
of  Sparks. 


sparks  across  a  carefully  arranged  spark-gap  between  metal 
balls ;  arrangements  being  made  to  blow  out  the  spark  with 
great  suddenness  by  the  application  of  a  magnetic  field  or 
of  an  air-blast  (Fig.  360).  Each  of  these  sudden  sparks,  of 

which  there  may  be  from 
2  or  3  up  to  100  or  so  per 
second  according  to  the  de- 
vices adopted,  sets  up  high- 
frequency  oscillations  in 
a  special  oscillating  circuit 
containing  capacity  and  in- 
ductance ;  and  it  is  usual  to 
pass  these  oscillations  through  the  primary  circuit  of  an 
oscillation-transformer  in  the  secondary  of  which  a  corre- 
sponding set  of  oscillations  is  induced  at  a  very  high  voltage. 
The  oscillation-transformer,  commonly  called  a  Tesla  coil,  has 
no  iron  core ;  its  coils  have  comparatively  few  turns ;  they 
must  be  highly  insulated  from  one  another,  and  are  usually 
immersed  in  oil.  They  are  often  provided  with  adjustable 
contacts  to  vary  the  number  of  turns  in  use ;  for  it  is  highly 
advantageous  to  tune  together  these  two  circuits. 

Fig.  361  is  a  generalized  diagram  of  a  Tesla  or  Elihu 
Thomson  apparatus.     G  is  an  alternator,  or  other  source 


FIG.  361.  —  Circuit  for  producing  High  Frequency  Discharge. 

such  as  a  battery  with  a  high-speed  break  (Art.  247),  supply- 
ing the  primary  of  an  ordinary  high-voltage  induction  coil  J 
(Art.  246).  The  secondary  of  the  induction  coil  excites  the 
spark  in  a  spark-gap  A  (or  in  a  pair  of  spark-gaps)  in  the 
oscillating  circuit  containing  a  condenser  (or  condensers)  C. 


CH.  xv.  604]    HIGH   FREQUENCY   DISCHARGES  611 

The  oscillation  transformer  PS  couples  together  the  oscilla- 
tion circuit  and  the  working  circuit  ;  there  being  provided  an 
adjustable  tuning  coil  or  connexion  L  in  one  or  both  of  these 
circuits.  If  a  second  spark-gap  B  is  arranged  in  the  working 
circuit,  long  sparks  of  high-frequency  may  be  observed. 

These  effects  can  be  much  augmented  by  increasing  the 
suddenness  of  the  spark  by  using  a  magnetic  field  (Art.  494) 
to  blow  it  out.  Elihu  Thomson  used  an  air-blast  across  the 
spark-gap  for  the  same  purpose. 

High-frequency    experiments    of    striking    character    can 
be  shown  with  such  apparatus.     If  one  of  the  terminals  of 
the  working  circuit  is  put  to  earth,  a  luminous  discharge  is 
seen  to  issue  from  the  other  terminal.     If 
the  terminals  of  the  working  circuit  are 
connected  together  by  an  arched  piece  of 
stout  copper  wire,  as  in  Fig.  362,  and  a 
small  glow-lamp  is  connected  across  the 
arch,  the  lamp  will  glow,  though  appar- 
ently short-circuited  :    the  impedance  of 
the  copper  arch,  owing  to  the  skin-effect 
(Art.  532),  will  be  greater  than  the  re-    Flo.  362.  _ 


sistance  of  the  glow-lamp.     The  physio-       showing  impedance  of 

r  J  Copper-wire  Loop. 

logical  effects  of  the  high-frequency  dis- 
charge are  remarkable  in  that  they  are  extraordinary  small. 
The  long  sparks  may  be  received  through  the  arm  or  body 
with  no  shock  or  painful  sensation  beyond  a  slight  feeling  of 
warmth.  A  small  glow-lamp  may  even  be  lighted  by  a  high- 
frequency  current  passing  through  the  human  body,  without 
any  unpleasant  sensation.  The  luminous  effects  produced 
in  vacuum  tubes  are  varied  and  very  brilliant. 

604.  Frequency  Measurer.  —  A  simple  frequency-meas- 
urer for  high-frequency  oscillations  may  be  made  of  a  circuit 
containing  an  open-wound  inductance  coil  of  40  or  50  turns 
of  wire  in  series  with  an  adjustable  condenser  and  a  minute 
glow-lamp  or  a  thermal  detector  (Art.  479).  Then  the  con- 
denser is  adjusted  until  the  glow-lamp  or  detector  indicates 


612 


ELECTRICITY   AND   MAGNETISM     [PT.  n.  605 


that  resonance  has  been  attained ;  and  the  frequency  can  be 
calculated  by  the  formula  of  Art.  600,  viz.  n  =  1  -r-  2  w  VCL. 

605.  Researches  of  Hertz.  —  In  1888  Heinrich  Hertz 
succeeded  in  producing  electromagnetic  waves  in  a  way  which 
permitted  him  to  examine  their  propagation  through  space, 
and  to  show  that  though  invisible,  they  resembled  ordinary 
waves  of  light.  They  possessed  many  of  the  same  properties, 
travelled  at  the  same  speed,  and  were  capable  of  being  re- 
flected, refracted,  polarized,  etc. 

Of  the  power  of  oscillatory  discharges  to  propagate  dis- 
turbances in  the  surrounding  space  something  was  already 


OSCILLATOR. 
FIG.  363. 


RESONATOR. 
FIG.  364. 


known.  Henry  had  shown  that  they  set  up  other  sparks 
in  distant  conducting  circuits.  It  had  been  discovered  1 
that  a  spark-gap  in  tjie  exciting  circuit  was  necessary.  Fitz- 
gerald had  definitely  proposed  to  start  waves  by  the  oscilla- 
tory discharges  of  small  condensers.  But  no  one  had  sys- 
tematically followed  out  the  phenomena  of  propagation  of 
the  waves. 

Hertz  employed  to  start  the  waves  an  apparatus  called 
an  oscillator  (Fig.  363),  consisting  of  two  metallic  conductors 
(balls  or  plates)  united  by  a  metal  rod,  at  the  middle  of 
which  was  interposed  a  spark-gap  between  two  well-polished 
knobs.  And  to  detect  the  waves  at  a  distance  he  employed 
a  resonator,  simply  a  circle  or  square  of  wire,  having  in  it  a 
spark-gap  capable  of  minute  adjustment.  In  one  experi- 
ment the  oscillator  consisted  of  two  zinc  plates  A  and  B 
(Fig.  363)  with  sides  40  cm.  long,  mounted  50  cm.  apart,  and 

1  See  paper  by  the  author  in  the  Philosophical  Magazine  (September, 
1876). 


CH.  xv.  605]  HERTZ'S  APPARATUS  613 

having  stout  copper  wires  leading  to  a  spark-gap  between 
very  brightly  polished  brass  balls.  A  dry  wood  stand  was  a 
sufficient  insulator.  The  resonator  to  match  was  a  wire 
circle  35  cm.  in  radius,  Fig.  364,  or  a  wire  square  of  60  cm. 
sides.  To  experiment  with  this  apparatus  the  oscillator 
is  joined  to  a  small  induction-coil.  When  a  spark  snaps 
across  the  gap  it  sets  up  a  temporary  conducting  path  for 
the  surgings  that  follow.  For  a  rush  of  current  from  left  to 
right  overcharges  the  right-hand  plate,  and  so  there  follows 
a  rush  back  from  right  to  left,  and  so  on.  Each  spark  sent 
by  the  coil  across  the  gap  consists  of  a  dozen  or  so  oscilla- 


FIG.  365.  —  Hertz's  Apparatus  for  Production  and  Detection  of  Electric  Waves. 

tions,  each  lasting  about  1/100,000,000  of  a  second,  the  period 
being  determined  (Art.  600)  by  the  capacity  and  inductance 
of  the  apparatus ;  the  discharges  surging  backward  and 
forward  from  A  to  B  until  they  die  out  (Fig.  356).  Let  the 
line  drawn  horizontally  in  Fig.  365  be  termed  the  base  line, 
and  let  the  line  AB  be  termed  the  line  of  oscillation.  Then  if 
the  resonator  is  placed  with  its  centre  on  the  base  line  at  a  few 
feet  away  from  the  oscillator  and  is  turned  into  various  posi- 
tions, various  effects  are  observed.  If  the  resonator  is  set 
edge-on  vertically,  no  sparks  are  observed  in  it  whatever 
the  situation  of  the  gap  in  the  circle.  If  it  is  laid  edge-on 
horizontally  sparks  pass  between  the  balls  of  the  resonator. 
These  are  brightest  when  the  gap-space  is  nearest  toward 
the  oscillator,  so  that  the  induced  spark  is  parallel  to  the 
primary  spark.  If  the  resonator  be  now  turned  broadside 


614  ELECTRICITY  AND  MAGNETISM      [PT.  n.  606 

on  to  the  oscillator  it  will  be  found  that  there  are  sparks  when 
the  gap  is  at  the  top  or  bottom  of  the  circle  —  so  that  the 
sparks  are  parallel  to  the  primary  spark ;  but  there  are  none 
if  the  gap  is  at  the  side.  The  primary  spark  does  not  here 
induce  sparks  at  right  angles  to  itself. 

The  reflexion  of  electric  waves  was  observed  in  various 
ways.  If  right  opposite  the  oscillator,  Fig.  365,  is  set  a  large 
metal  sheet  as  a  reflector,  to  send  back  the  waves  that  pass 
along  the  base  line,  stationary  nodes  will  be  produced  at 
regular  intervals.  If  the  resonator  is  put  broadside  on, 
with  its  gap  at  the  highest  point,  and  moved  along  the  base 
line  till  it  lies  flat  against  the  reflector,  there  will  in  this  posi- 
tion be  no  sparks ;  but  if  it  is  slowly  moved  back  from  the 
sheet  sparks  will  show,  will  come  to  a  maximum,  then  die 
out  as  the  first  node  is  reached  at  about  180  cm.  from  the 
reflector.  Passing  this  node  the  sparks  will  begin  again, 
nodes  occurring  at  equal  intervals  apart  along  the  base  line. 
By  using  large  parabolic  mirrors  Hertz  showed  that  these 
electric  waves  can  be  reflected  and  brought  to  a  focus  exactly 
as  light- waves  can  be.  Hertz  also  showed  refraction  with  a 
prism  of  pitch;  and  polarization  by  means  of  gratings  of 
parallel  wires. 

606.  Detectors  of  Electric  Waves.  —  The  Hertz  spark- 
gap  resonator  is  only  one  means  of  detecting  electric  waves. 
A  prepared  frog's  leg  (Art.  271)  may  be  used  instead  of  a 
spark-gap.  A  sensitive  vacuum-tube,  especially  if  primed 
by  application  with  a  battery  of  some  hundreds  of  small 
cells  not  quite  able  of  themselves  to  start  a  spark,  forms  a 
good  explorer.  Electrometers;  thin  wires  capable  of  ex- 
panding when  heated  by  the  induced  currents ;  and  gal- 
vanometers in  parallel  with  the  minute  air-gap  in  the  reso- 
nator, are  amongst  the  possible  means.  Branly  in  1890  found 
metallic  powders  to  be  sensitive.  A  good  form  is  a  tube 
partly  filled  with  metallic  filings,  Fig.  366,  inserted  in  circuit 
with  a  galvanometer  and  a  single  cell.  The  resistance  of  the 
filings  is  very  great,  and  little  current  flows,  until  an  electric 


CH.  xv.  607]      PROPERTIES   OF   ELECTRIC   WAVES       615 

wave  impinges  upon  the  tube,  when  at  once  the  filings  con- 
duct (compare  Art.  432  on  conductance  of  powders).  On 
lightly  tapping  the  tube  the  filings  fall  back  into  their  former 
state.  Using  such  a  detector,  called  a  coherer,  and  an  oscil- 
lator consisting  of  a  highly  polished  brass  ball  between  two 
smaller  balls,  Lodge  in  1894  publicly  showed  how  these  elec- 
tric waves  can  pass  hundreds  of  feet 
through  walls  and  floors  of  houses 
and  can  convey  wireless  signals.  Filings' 

This  invention  was  the  basis  of  so-      FlG" 366'  ~  Filings  Coherer> 
called  wireless  telegraphy;  the  coherer  current  being  used  in 
turn  to  operate  a  telegraphic  receiver  (see  Art.  582). 

607.  Properties  of  Electric  Waves.  —  The  universal 
equation  connecting  frequency  n,  wave-length  A.,  and  velocity 
of  propagation  v  is :  v  =  n\.  Taking  v  (in  air)  as  3  X  1010 
(cms.  per  sec.)  as  the  velocity  of  light,  and  the  measured 
length  of  the  red  waves  (the  longest  visible)  as  0-000076  cm., 
it  follows  that  the  frequency  of  oscillation  of  these  must  be 
no  less  than  395  X  1012  per  second.  The  waves  artificially 
produced  by  electric  oscillations  are  of  much  lower  frequency 
than  these,  and  their  wave-length  proportionally  longer. 
Their  wave-length  depends  on  the  size  of  the  apparatus  used 

as  oscillator,  just  as  the  note  emitted 
by  an  iron  cylinder  when  struck  on 
,  its  end  depends  on  the  length  of  the 

y  ifl  ^  f  T        cylinder.    The  wave-length  of  waves 

^fc^?^'  emitted  from  an  oscillator  consist- 

' "  ^  ___JL      *n£  °^  a  w*re  w*tk  a  smaU  capacity 

"'"""•ll"""11""1 """'""""I1     at  each  end  is  twice  the  length  of  the 

|p  V     wire.     That  of  waves  'emitted  from 

;;  a  sphere  (Fig.  367)  of  diameter  d  is 

2  ird/  V3  or  3-6  d ;  but  they  die  out 

FIG.  367. -Lodge's  Oscillator.  '  J 

after  about  1  vibration.  Righi  sug- 
gested the  form  of  oscillator  having  a  principal  spark-gap 
between  two  large  polished  spheres,  placed  between  two 
smaller  spheres.  If  the  oscillations  are  not  to  radiate  away 


SHI 


616 


ELECTRICITY  AND   MAGNETISM      [PT.  n.  608 


FIG.  368.  —  Experiment  illus- 
trating Impedance  of  Wire- 
Loop. 


their  energy  too  quickly,  the  oscillator  must  not  have  so 
large  a  fraction  of  its  charging  surface  exposed.  Hertz's 
oscillator,  Fig.  363,  resembles  a  Leyden  jar  with  its  coatings 
opened  out  widely  apart.  If  they  were  bent  round  to  face 
one  another  they  would  act  as  an  air- 
condenser  of  somewhat  larger  capacity. 
But  such  an  oscillator  would  radiate 
less  freely  and  would  maintain  a  longer 
train  of  waves. 

The  currents  produced  in  wires  by 
oscillations  of  such  enormous  fre- 
quency are  only  skin-currents  (Art. 
532),  the  inner  part  of  the  wire  being 
idle.  Hence  for  such  currents  the  im- 
peding resistance  of  a  stout  copper  wire  may  be  millions  of 
ohms.  One  evidence  of  this  is  afforded  by  the  tendency  to 
lateral  discharge.  This  is  readily  shown  by  connecting  be- 
tween the  Leyden  jars  of  an  influence  machine  a  loop  of  stout 
copper  wire  bent  as  in  Fig.  368.  When  a  discharge  takes 
place  between  the  knobs,  there  will  be  an  oscillatory  current 
set  up  between  the  outer  coatings  also ;  and  this  oscillatory 
current  rather  than  flow  along  the  metal  loop  will  jump  as  a 
spark  across  the  parts  that  lie  nearest  together. 
The  tendency  of  lightning  to  produce  lateral 
discharges  is  relied  upon  by  Lodge  in  his  con- 
tention as  to  the  oscillatory  character  of  the 
flash  (Art.  356). 

608.  Travelling  of  Waves  along  Wires.  —  If 
an  oscillatory  spark  is  sent  into  one  end  of  a 
long  wire,  by  the  time  that  the  second  pulsa- 
tion reaches  its  maximum  the  first  will  have 
travelled  a  certain  distance  which  may  be  called 
the  wave-length  of  the  disturbance.  According 
to  Maxwell's  theory  (Art.  609)  the  velocity  of  propagation 
will  be  equal  to  that  of  light,  the  energy  really  travelling 
through  the  air,  and  settling  down  laterally  into  the  wire.  It 


G     C 


FIG.  369.  —  Von 
Bezold's  Ex- 
periment. 


CH.  xv.  609]     ELECTROMAGNETIC   THEORY  617 

appears  from  experiment  that  the  velocity  of  a  wave  guided 
by  a  wire  is  the  same  as  that  of  a  wave  travelling  in  free  air. 
That  the  speed  of  travelling  is  independent  of  the  thickness  or 
materials  of  the  wire  was  proved  in  1870  by  Von  Bezold,  using 
the  device  of  Fig.  369.  Let  an  oscillatory  discharge  be  sent 
by  a  wire  at  G  into  a  rectangular  circuit  ABCD,  having 
a  spark-gap  PQ  midway  between  B  and  D.  It  is  evident 
that  if  G  is  midway  between  A  and  C  the  impulses  will  arrive 
simultaneously  at  P  and  Q  if  both  sides  of  the  system  are 
alike  ;  and  there  will  be  no  spark.  If  now  one  side,  say  CD, 
be  made  of  iron  and  the  other,  AB,  of  copper,  it  will  be  found 
that  still  the  discharge  must  be  led  in  at  G,  exactly  midway, 
if  there  is  to  be  no  spark. 


LESSON  LIX.  —  The  Electromagnetic  Theory  of  Light 

609.  Maxwell's  Theory.  —  In  1864  Clerk  Maxwell  put 
forward  the  theory  that  the  waves  of  light  are  not  mere 
mechanical  motions  of  the  ether,  but  that  they  are  electrical 
undulations.  These  undulations  are  partly  electrical  and 
partly  magnetic,  oscillating  electrical  displacements  being 
accompanied  by  oscillating  magnetic  fields  at  right  angles 
to  them,  whilst  the  direction  of  propagation  of  the  wave  is  at 
right  angles  to  both.  According  to  this  theory  the  phenom- 
ena of  electromagnetism  and  the  phenomena  of  light  are 
all  due  to  certain  modes  of  motion  in  the  ether,  electric  cur- 
rents and  magnets  being  due  to  streams  and  whirls  or  other 
bodily  movements  in  the  substance  1  of  the  ether,  while  light 
is  due  to  vibrations  to  and  fro  in  it. 

An  electric  displacement  during  its  growth  or  decay 
produces  a  magnetic  force  at  right  angles  to  itself ;  it  also 
produces  (by  the  peculiar  action  known  as  induction)  an 
electric  force  which  is  propagated  at  right  angles  both  to  the 
electric  displacement  and  to  the  magnetic  force.  Now  it  is 

1  Or,  as  we  should  now  say,  movements  of  the  electrons  in  the  ether ; 
the  ether  itself  being  relatively  at  rest.  See  Art.  630. 


618  ELECTRICITY   AND   MAGNETISM       [PT.  n.  609 

known  that  in  the  propagation  of  light  the  actual  displace- 
ments or  vibrations  which  constitute  the  so-called  ray  of  light 
are  executed  in  directions  at  right  angles  to  the  direction  of 
propagation.  This  analogy  is  an  important  point  in  the 
theory,  and  immediately  suggests  the  question  whether  the 
respective  rates  of  propagation  are  the  same.  Now  the 
velocity  of  propagation  of  electromagnetic  induction  is  that 
velocity  "  v  "  which  was  shown  (Art.  386)  to  represent  the 
ratio  between  the  electrostatic  and  the  electromagnetic 
units,  and  which  (in  air)  has  been  found  to  be 

2-999  X  1010  centimetres  per  second. 

And  the  velocity  of  light  (in  air)  has  been  repeatedly  meas- 
ured (by  Fizeau,  Cornu,  Michelson,  and  others)  (see  p.  348), 
giving  as  the  approximate  value 

2-9986  X  1010  centimetres  per  second. 

From  the  equations  for  the  propagation  of  a  disturb- 
ance in  an  electromagnetic  medium,  having  dielectric  co- 
efficient k  (Art.  315)  and  permeability  //.  (Art.  390),  it  was 
calculated  by  Maxwell  that  the  velocity  ought  to  be  numeri- 
cally =  1  V/^i.  And,  as  we  have  seen,  this  quantity  enters 
into  the  ratio  of  the  units  (Art.  387),  and  can  be  calculated 
from  them.  It  follows  that  if  there  are  two  transparent 
media  of  equal  permeability  but  different  dielectric  capacities, 
the  velocities  in  them  ought  to  vary  relatively  inversely  as 
Vfc.  But  the  ratio  of  the  velocities  of  light  in  them  is  called 
their  refractive  index.  Hence  if  Maxwell's  theory  is  true, 
the  dielectric  capacity  of  ordinary  transparent  media  ought 
to  be  equal  to  the  square  of  the  refractive  index.  Experi- 
ments by  Gordon,  Boltzmann,  and  others,  show  this  to  be 
approximately  true  for  waves  of  great  wave-length.  The 
values  are  shown  below.  For  gases  the  agreement  is  even 
closer. 


CH.  xv.  610]  ENERGY   PATHS  619 


K 

SQUARE  OF  INDEX 

Flint  Glass       
Bisulphide  of  Carbon    .     . 
Sulphur  (mean)    .... 
Paraffin 

3-162 
1-812 
4-151 
2'32 

2-796 
2*606 
4-024 
2'33 

Another  consequence  of  the  theory  is  that  all  conduc- 
tors, since  they  dissipate  the  energy  of  the  currents  set  up 
in  them,  ought  to  be  opaque  to  light.  Metallic  conductors 
are  so,  except  when  in  very  thin  films.  But  electrolytic 
liquids  are  not  opaque,  the  mechanism  of  their  conduction  be- 
ing different  (Art.  569).  In  some  crystalline  bodies  which 
conduct  electricity  better  in  one  direction  than  in  another, 
the  opacity  to  light  differs  correspondingly.  Coloured  crys- 
tals of  tourmaline  conduct  electricity  better  across  the  long 
axis  of  the  crystal  than  along  that  axis.  Such  crystals  are 
much  more  opaque  to  light  passing  along  the  axis  than 
to  light  passing  across  it.  And,  in  the  case  of  rays 
traversing  the  crystal  across  the  axis,  the  vibrations  across 
the  axis  are  more  completely  absorbed  than  those  parallel 
to  the  axis  :  whence  it  follows  that  the  transmitted  light  will 
be  polarized. 

Maxwell's  theory  was  therefore  considered  in  this  country 
as  an  established  truth  for  some  years  before  Hertz's  striking 
researches  of  1888  gave  experimental  proof  of  a  direct  kind. 

610.  Energy  Paths.  —  From  Maxwell's  equations  Poyn- 
ting  in  1883  drew  the  conclusion  that  in  all  cases  where  energy 
is  transferred  in  an  electric  system  it  flows  parallel  to  the 
surfaces  of  both  electric  and  magnetic  equipotentials.  What 
we  call  an  electric  current  along  a  wire  is  rather  a  transfer  of 
energy  by  an  invisible  mechanism  in  the  medium  outside  the 
wire.  Wherever  in  the  wire  there  as  resistance,  wasting 
energy  by  degrading  it  into  heat,  at  that  point  energy  flows 
in  laterally  from  the  medium.  According  to  this  view,  the 
service  of  the  wire  is  merely  to  guide  the  energy  flow  going  on 


620  ELECTRICITY  AND   MAGNETISM     [PT.  n.  611 

outside  it.1  We  know  that  when  a  current  is  started  much 
energy  is  spent  in  building  up  around  the  conductor  a  mag- 
netic field,  the  amount  spent  being  |  Li2  (Art.  501).  When 
the  circuit  is  "  broken  "  this  energy  flows  back  laterally  into 
the  wire,  giving  rise  to  the  so-called  extra-current  sparks. 
According  to  Poynting's  view,  which  has  been  independ- 
ently elaborated  by  Heaviside,  all  energy  flows  in  similarly. 
In  the  case  of  the  transfer  of  energy  in  an  alternating-current 
transformer  from  the  coils  of  the  primary  circuit  to  those  of 
the  secondary,  it  is  pretty  obvious  that  the  flow  of  energy 
must  take  place  laterally  to  the  copper  wires;  and  it  also 
takes  place  laterally  to  the  iron  wires  of  the  core,  though  this 
is  not  so  obvious. 

LESSON  LX.  —  Other  Relations  between  Light  and  Electricity 

611.  Electro-optical  Phenomena.  —  Several  important  re- 
lations have  been  observed  between  electricity  and  light. 
These  observations  may  be  thus  classified  under  the  follow- 
ing heads : — 

(i.)  Production  of  double  refraction  by  dielectric  stress, 
and  by  magnetic  stress. 

(ii.)  Rotation  of  plane  of  polarization  of  a  wave  of  light  on 
traversing  a  transparent  medium  placed  in  a  mag- 
netic field,  or  by  reflexion  at  the  surface  of  a  magnet. 

(iii.)  Change  in  frequency  of  trie  light  radiated  (or  ab- 
sorbed) by  atoms  in  a  magnetic  field. 

(iv.)  Change  of  electric  resistance,  exhibited  by  selenium 
and  other  bodies  during  exposure  to  light. 

(v.)    Photo-chemical  excitation  of  electromotive-forces. 

(vi.)  Relation  between  refractive  index  and  dielectric 
capacity  of  transparent  bodies. 

(vii.)  Electric  effect  of  ultra-violet  light. 

It  was  announced  by  Mrs.  Somerville,  by  Zantedeschi,  and 
others,  that  steel  needles  could  be  magnetized  by  exposing  portions 

1  See  particularly  Sir  Oliver  Lodge's  Modern  Views  of  Electricity. 


CH.  xv.  612,  613]  ELECTRO-OPTICAL  EFFECTS  621 

of  them  to  the  action  of  violet  and  ultra-violet  rays  of  light;    the 
observations  were,  however,  erroneous. 

Bidwell  found  that  light  falling  upon  a  recently  demagnetized 
piece  of  iron  produces  an  instantaneous  revival  of  magnetism. 

612.  Electrostatic    Optical    Stress.  —  In    1875    Dr.    Kerr 
of  Glasgow  discovered  that  glass  when  subjected  to  a  severe 
electrostatic  stress  undergoes  an  actual  strain,  which  can 
be  observed  by  the  aid  of  a  beam  of  polarized  light.     In  the 
original  experiment  two  wires  were  fixed  into  holes  drilled 
in  a  slab  of  glass,  but  not  quite  meeting,  so  that  when  these 
were  placed  in  connexion  with  the  terminals  of  an  induction 
coil  or  of  an  influence  machine  the  accumulating  charges  on 
the  wires  subjected  the  intervening  dielectric  to  an  electro- 
static tension  along  the  electric  lines  of  force.     The  slab 
when  placed  between  two  Nicol  prisms  as  polarizer  and  analy- 
ser l  exhibited  double  refraction,  as  if  it  had  been  subjected 
to  a  pull  and  had  expanded  along  the  direction  of  the  electric 
force.     Bisulphide  of  carbon  and  other  insulating  liquids 
exhibit  similar  phenomena,  but  fatty  oils  of  animal  and 
vegetable  origin  exhibit  an  action  in  the  negative  direction, 
as  if  they  had  contracted  along  the  electric  lines.     It  is 
found  that  the  difference  of  retardation  between  the  ordinary 
and  extraordinay  waves  per  unit  thickness  of  the  dielectric  is 
proportional  to  the  square  of  the  resultant  electric  force.     The 
axis  of  double  refraction  is  along  the  line  of  the  electric  force. 
Quincke  has  pointed  out  that  these  phenomena  can  be  ex- 
plained by  the  existence  of   electrostatic  expansions  and 
contractions,  stated  in  Art.  320. 

613.  Magneto-optic  Rotation  of  the  Plane  of  Polarization 
of  Light,  —  In  1845  Faraday  discovered  that  a  wave  of  light 
polarized  in  a  certain  plane  can  be  twisted  round  by  the  ac- 
tion of  a  magnet,  so  that  the  vibrations  are  executed  in  a 
different  plane.     The  plane  in  which  a  beam  is  polarized  can 

1  A  ray  of  light  is  said  to  be  polarized  if  the  vibrations  take  place  in  one 
plane.  Ordinary  light  can  be  reduced  to  this  condition  by  passing  it  through 
a  suitable  polarizing  apparatus  (such  as  a  Nicol  prism,  a  thin  slice  of  tour- 
maline crystal,  etc.). 


G22  ELECTRICITY  AND   MAGNETISM      [PT.  n.  613 

be  detected  by  observing  it  through  a  second  Nicol  prism 
(or  tourmaline),  for  each  such  polarizer  is  opaque  to  waves 
polarized  in  a  plane  at  right  angles  to  that  plane  in  which  it 
would  itself  polarize  light.  Faraday  caused  a  polarized 
beam  to  pass  through  a  piece  of  a  certain  "  heavy  glass  " 
(consisting  chiefly  of  borate  of  lead),  lying  in  a  powerful  mag- 
netic field,  between  the  poles  of  a  large  electromagnet, 
through  the  coils  of  which  a  current  could  be  sent.  In  the 
path  of  the  emerging  beam  was  placed  as  analyser  a  second 
Nicol  prism  which  had  been  turned  round  until  all  the 
light  was  extinguished.  In  this  position  its  own  plane  of 
symmetry  was  at  right  angles  to  the  plane  of  polarization 
of  the  beam.  On  completing  the  circuit,  light  was  at  once 
seen  through  the  analysing  Nicol  prism,  proving  that  the 
waves  had  been  twisted  round  into  a  new  position,  in  which 
the  plane  of  polarization  was  no  longer  at  right  angles 
to  the  plane  of  symmetry  of  the  analyser.  But  if  the  analys- 
ing Nicol  prism  was  itself  turned  round,  a  new  position 
could  be  found  (at  right  angles  to  the  plane  of  polarization 
of  the  waves)  at  which  the  light  was  once  more  extinguished. 
The  direction  of  the  magneto-optic  rotation  of  the  plane  of 
polarization  is  the  same  (for  diamagnetic  media)  as  that  in 
which  the  current  flows  which  produces  the  magnetism.  Verdet 
discovered  the  important  law  that,  with  a  given  material, 
the  amount  of  rotation  is  proportional  to  the  strength  of  the 
magnetic  field  §.  In  case  the  waves  do  not  pass  straight 
along  the  direction  of  the  field,  the  amount  of  rotation  is 
proportional  to  the  cosine  of  the  angle  ft  between  the  direction 
of  the  beam  and  the  lines  of  force.  It  is  also  proportional  to 
the  length  I  of  the  material  through  which  the  waves  pass.  These 
laws  are  combined  in  the  equation  for  the  rotation :  0  = 
w  §  cos  (31 ;  where  w  is  a  coefficient  which  represents  the  specific 
magnetic  rotatory  power  of  the  given  substance,  and  is  known 
as  Verdet' s  constant.  Now,  §  cos  fil  is  the  difference  of  mag- 
netic potential  between  the  point  A  where  the  wave  enters 
and  B  where  it  leaves  the  medium.  Hence  w  =  -z-0  (Vs  —  VA). 


CH.  xv.  613]      MAGNETO-OPTICAL   EFFECTS  623 

The  value  of  Verdet's  constant  for  yellow  sodium  light, 
at  18°  C.,  has  been  carefully  determined.  Its  value  (in  ra- 
dians per  unit  fall  of  magnetic  potential)  is,  in  bisulphide 
of  carbon  1-222  X  10~5;  in  water  0-375  X  10~5;  in  heavy 
glass  2-132  X  10~5.  For  diamagnetic  substances  the  coeffi- 
cient is  usually  positive ;  but  in  the  case  of  many  magnetic 
substances,  such  as  solutions  of  ferric  chloride,  has  a  nega- 
tive value  (i.e.  in  these  substances  the  rotation  is  in  the  oppo- 
site direction  to  that  in  which  the  magnetizing  current  flows) . 
For  light  of  different  colours  the  rotation  is  not  equal,  but 
varies  very  nearly  inversely  as  the  square  of  the  wave-length. 

Gases  also  rotate  the  plane  of  polarization  of  light  in 
a  magnetic  field  with  varying  amounts ;  coal-gas  and  car- 
bonic acid  being  more  effective  than  air  or  hydrogen ;  oxy- 
gen and  ozone  being  negative.  The  rotation  is  in  all  cases 
very  slight,  and  varies  for  any  gas  in  proportion  to  the 
quantity  of  gas  traversed.  H.  Becquerel  showed  that  the 
plane  of  the  natural  polarization  of  the  sky  does  not  coincide 
with  the  plane  of  the  sun,  but  is  rotated  by  the  influence  of 
the  earth's  magnetism  through  an  angle  which,  however,  only 
reached  59'  of  arc  at  a  maximum  on  the  magnetic  meridian. 

We  have  seen  (Arts.  127,  429,  and  430)  what  evidence  there  is 
for  thinking  that  magnetism  is  a  phenomenon  of  rotation,  there 
being  a  rotation  of  something  around  an  axis  lying  in  the  direction 
of  the  magnetization.  Such  a  theory  would  explain  the  rotation 
of  the  plane  of  polarization  of  a  ray  passing  through  a  magnetic 
field.  For  a  ray  of  plane-polarized  light  may  be  conceived  of  as 
consisting  of  a  pair  of  (oppositely)  circularly-polarized  waves,  in 
which  the  right-handed  rotation  in  one  ray  is  periodically  counter- 
acted by  an  equal  left-handed  rotation  in  the  other  ray;  and  if 
such  a  motion  were  imparted  to  a  medium  in  which  there  were 
superposed  a  rotation  (such  as  we  conceive  to  take  place  in  every 
magnetic  field)  about  the  same  direction,  one  of  these  circularly- 
polarized  rays  would  be  accelerated  and  the  other  retarded,  so 
that,  when  they  were  again  compounded  into  a  single  plane- 
polarized  ray,  this  plane  would  not  coincide  with  the  original  plane 
of  polarization,  but  would  be  apparently  turned  round  through  an 
angle  proportional  to  the  superposed  rotation. 


624          ELECTRICITY  AND   MAGNETISM    [PT.  n.  614-616 

614.  Kerr's  Effect.  —  Dr.  Kerr  showed  in  1877  that  a  ray 
of  polarized  light  is  also  rotated  when  reflected  at  the  surface 
of  a  magnet  or  electromagnet.     When  the  light  is  reflected 
at  a  pole  the  plane  of  polarization  is  turned  in  a  direction 
contrary  to  that  in  which  the  magnetizing  current  flows. 
If  the  light  is  reflected  at  a  point  on  the  side  of  the  magnet  it 
is  found  that  when  the  plane  of  polarization  is  parallel  to  the 
plane  of  incidence  the  rotation  is  in  the  same  direction  as  that 
of  the  magnetizing  current ;  but  that,  when  the  plane  of  polar- 
ization is  perpendicular  to  the  plane  of  incidence,  the  rotation 
is  in  the  same  direction  as  that  of  the  magnetizing  current 
only  when  the  incidence  exceeds  75°,  being  in  the  opposite 
direction  at  lesser  angles  of  incidence. 

615.  Kundt's  Effect.  —  Kundt  found  that  the  plane  of 
polarization  of  light-waves  is  also  rotated  if  the  light  is  passed 
through  a  film  of  iron  so  thin  as  to  be  transparent,  if  placed 
transversely  in  a  magnetic  field. 

616.  Zeeman   Effect.  —  In    1896   P.   Zeeman   discovered 
that  when  a  source  of  light  is  placed  in  a  magnetic  field  the 
nature  of  the  emitted  light  undergoes  certain  modifications. 
In  the  simplest  case,  when  the  light  is  that  of  an  incandes- 
cent vapour  the  spectrum  of  its  rays  consists  of  certain  char- 
acteristic bright  lines.     But  when  the  source  of  the  light  is 
magnetized  the  spectrum  lines  are  split  into  two  or  three 
component  lines  so  close  together  that  a  spectroscope  of  the 
highest  resolving  power  is  required  to  detect  them.     Ex- 
amined in  a  direction  parallel  to  the  magnetic  field  are  ob- 
served two   lines ;    their  light  being   circularly  polarized  in 
opposite  directions.     Examined  in  a  direction  normal  to  the 
field  three  components  are  observed  ;  the  light  of  the  middle 
one  being  found  to  be  polarized  normally  to  the  field,  while 
the  outer  lines  of  the  triplet  are  polarized  in  a  plane  parallel 
to  the  field.     The  dark  lines  in  absorption  spectra  are  simi- 
larly split.     These  phenomena  can  be  interpreted  in  terms 
of  the  theory  that  the  emission  is  due  to  the  motions  of  elec- 
trons in  the  atom  (Art.  637),  as  predicted  by  Lorentz. 


CH.  xv.  617,  618]       PHOTO-ELECTRIC   EFFECTS  625 

617.  Photo-electric    Properties    of    Selenium.  —  In    1873 
Willoughby  Smith  announced  the  discovery  (by  J.   E.  May- 
hew)    that   the   element   selenium   possesses   the    abnormal 
property  of  changing  its  electric  resistance  under  the  influ- 
ence of  light.     Ordinary  fused  or  vitreous  selenium  is  a  very 
bad  conductor;    its  resistance  being  nearly  forty-thousand- 
million  (3-8  X  1010)  times  as  great  as  that  of  copper.     When 
carefully  annealed  (by  keeping  for  some  hours  at  a  tempera- 
ture of  about  220°  C.,  just  below  its  fusing  point,   and  sub- 
sequent slow  cooling)  it  assumes  a  crystalline  condition,  in 
which  its  electric  resistance  is  considerably  reduced.     In  the 
latter  condition,  especially,  it  is  sensitive  to  light.     Adams 
found  that  greenish-yellow  rays  were  the  most  effective.     He 
also  showed  that  the  change  of  electric  resistance  varies  directly 
as  the  square  root  of  the  illumination,  and  that  the  resistance 
is  less  with  a  high  electromotive-force  than  a  low  one.     In 
1879  Graham  Bell  and  Sumner  Tainter  devised  "  selenium  " 
cells,  in  which  annealed  selenium  is  formed  into  narrow  strips 
between  the  edges  of  broad  conducting  plates  of  brass,  thus 
securing  both  a  reduction  of  the  transverse  resistance  and  a 
large  amount   of  surface-exposure   to   light.     Thus   a   cell, 
whose  resistance  in  the  dark  was  300  ohms,  when  exposed  to 
sunlight  had  a  resistance  of  but  150  ohms.     This  property  of 
selenium  these  investigators  applied  in  the  construction  of 
the  Photophone,  an  instrument  which  transmits  sounds  to 
a  distance  by  means  of  a  beam  of  light  reflected  to  a  distant 
spot  from  a  thin  mirror  thrown  into  vibrations  by  the  voice ; 
the  beam  falling,  consequently,  with  varying  intensity  upon  a 
receiver  of  selenium  connected  in  circuit  with  a  small  battery 
and  a  Bell  telephone  receiver  (Art.  593)  in  which  the  sounds 
are  reproduced  by  the  variations  of  the  current.     Selenium 
cells  have  been  used  in  the  electric  transmission  of  pictures. 

Similar  properties  are  possessed,  to  a  smaller  degree,  by 
tellurium.     Carbon  is  also  sensitive  to  light. 

618.  Photo-chemical   Cells.  —  About  the  middle  of  last 
century  Edmond  Becquerel  showed  that  when  two  plates  of 

2s 


626  ELECTRICITY  AND   MAGNETISM      [PT.  n.  619 

silver,  coated  with  freshly-deposited  chloride  of  silver,  are 
placed  in  a  cell  with  water  and  connected  with  a  galvanom- 
eter, a  current  is  observed  to  pass  when  light  falls  upon  one 
of  the  two  plates,  the  exposed  plate  acting  as  an  anode. 

619.  Photoelectric  Loss  of  Charge.  —  In  1887  Hertz 
made  the  discovery  that  a  spark  starts  more  readily  between 
the  balls  of  a  discharger  when  illuminated  by  light  that  is 
rich  in  violet  and  ultra-violet  rays  (magnesium  light,  arc 
light,  or  spark  of  induction  coil)  than  when  not  so  illuminated. 
The  effect  varies  with  different  metals,  with  their  cleanness, 
the  nature  of  the  surrounding  gas,  with  the  kind  of  charge, 
and  with  the  polarization  of  the  light.  In  ultra-violet  light 
freshly  polished  zinc  in  air  rapidly  discharges  a  negative 
charge,  but  not  a  positive  one.  On  the  other  hand  the  perox- 
ides, in  an  atmosphere  of  hydrogen,  when  so  illuminated  read- 
ily discharge  positive  charges.  The  effect  is  stronger  when 
the  plane  of  the  vibration  of  the  incident  waves  is  at  right 
angles  to  the  surface  than  when  the  polarization  is  in  a  parallel 
plane.  The  phenomenon  appears  to  be  due  to  the  short 
light-waves  stimulating  chemical  reactions  which  do  not 
occur  except  (Art.  345)  by  a  species  of  electric  exchange.  In 
a  strong  magnetic  field  no  such  discharges  occur.  Hall- 
wachs  charged  clean  zinc  plates  positively  by  exposure  to 
ultra-violet  light.  Elster  and  Geitel  found  that  the  most 
oxidizable  and  electropositive  metals,  rubidium,  potassium, 
sodium,  are  also  the  most  active  photo-electrically,  and  dis- 
charge negative  charges  in  ordinary  daylight.  Observations 
are  best  made  in  a  vacuous  bulb.  If  in  such  a  tube  there  is 
introduced  a  second  unilluminated  metal  plate,  while  a  con- 
stant difference  of  potential  is  maintained  between  them,  a 
current  may  be  observed  to  pass  from  one  plate  to  the  other, 
the  intensity  of  the  photo-electric  current  increasing  with  the 
intensity  of  the  illumination. 


CHAPTER  XVI 

WIRELESS    TELEGRAPHY 

LESSON   LXI.  —  Radiotelegraphy  and  Radiotelephony 

620.  Principles  of  Wireless  Telegraphy.  —  We  have  seen 
(Art.  601)  how  Hertzian  waves  can  be  emitted  from  appara- 
tus producing  electric  oscillations  by  the  sudden  disturbance 
by  a  spark  passing  an  air-gap.  An  apparatus  that  thus  emits 
electromagnetic  waves  is  called  a  radiator  or  sender.  These 
waves  are  conveyed  by  the  ether  in  all  directions  at  the  speed 
of  light.  They  can  be  detected  at  a  distance,  even  through 
solid  walls,  by  a  suitable  detector,  working  a  galvanometer 
or  a  sensitive  telegraphic  receiver  or  a  receiving  telephone. 

When  these  points  are  understood  it  is  obvious  that  by 
sending  off  from  the  radiator  successive  flights  of  waves,  by 
using  a  Morse  key  to  make  impulses  of  long  or  short  duration, 
definite  signals  of  the  dash-and-dot  alphabet  of  Morse  can  be 
transmitted.  Such  wireless  transmission  of  signals  is  officially 
termed  radiotelegraphy. 

In  1894  Sir  Oliver  Lodge  first  publicly  showed  the  wireless 
transmission  of  dots  and  dashes.  His  oscillator  or  sender  was 
that  shown  in  Fig.  357;  his  receiver  was  a  filings  coherer 
resembling  Fig.  366,  provided  with  a  tapper,  acting  to  relay 
the  impulses  to  an  electric  bell,  or  a  galvanometer,  or  (later) 
to  a  siphon  recorder.  These  signals  were  sent  from  one  build- 
ing to  another  across  intervening  space  and  through  stone 
walls. 

In  1895  Sir  Ernest  Rutherford  invented  the  magnetic 
detector  depending  on  the  influence  of  Hertz  waves  on  the 
magnetic  state  of  a  newly  magnetized  wire  of  steel,  and  de- 
tected waves  at  over  half  a  mile  distance. 

627 


628  ELECTRICITY  AND   MAGNETISM      [PT.  n.  621 

In  1896  Guglielmo  Marconi,  using  a  Righi  oscillator 
(Art.  607)  and  a  filings  coherer  (Art.  606)  proposed  to  trans- 
mit signals  by  waves  which  he  supposed  to  be  new,  but  which 
turned  out  to  be  merely  Hertz  waves ;  and  he  suggested  vari- 
ous details  to  render  more  certain  the  action  of  the  apparatus ; 
and  in  particular  he  introduced  the  employment  of  insulated 
elevated  conductors  as  antennae  (Art.  621)  at  the  sending 
and  receiving  stations.  His  system  was  not  syntonic.  In 
1899,  using  the  apparatus  mentioned  above,  he  succeeded  in 
sending  messages  across  the  English  Channel. 

In  1900  a  new  method  of  using  a  telephone  receiver  in  con- 
junction with  a  mercury  and  carbon  coherer,  so  as  to  listen 
to  short  and  long  sounds  corresponding  to  dots  and  dashes, 
was  invented  by  Paolo  Castelli,  and  this  telephonic  method 
of  reception  has  largely  superseded  the  telegraphic  methods. 
In  1901,  using  Castelli's  telephonic  method,  Marconi  detected 
in  Newfoundland  signals  sent  from  Cornwall,  where  he  had 
erected  a  transmitting  station  with  an  alternator  generating 
powerful  spark  discharges. 

In  1897  Sir  Oliver  Lodge  pointed  out  that  for  syntonic 
working  it  was  necessary  to  employ  transmitting  apparatus 
that  emits  trains  of  waves,  otherwise  it  is  useless  to  try  to 
tune  the  receiving  apparatus  into  resonance  with  the  sender ; 
and  he  devised  arrangements  containing  capacity  and  in- 
ductance to  tune  the  circuits  together.  He  also  introduced 
the  use  of  an  oscillation  transformer  (Art.  603)  to  intervene 
between  the  receiving  capacity  or  area  and  the  coherer. 

By  resort  to  such  tuning  devices,  and  organizing  very 
powerful  transmitting  stations,  using  many  horse-power, 
Marconi  has  since  been  able  to  signal  thousands  of  miles 
to  distant  lands,  and  he  has  established  an  excellent  service 
between  ships  at  sea. 

621.  Radiotelegraphic  Transmitters.  —  In  a  modern 
"  wireless  "  station  the  sending  apparatus  consists  of  an 
aerial  system  of  wires  stretched  between  elevated  supports 
to  form  a  "  capacity  area,"  from  which  conductors  are  led 


CH.  xvi.  622] 


RADIOTELEGRAPHY 


629 


down,  through  a  tuning  inductance-coil  and  through  the 
secondary  of  an  oscillation  transformer  (Art.  603),  to  the 
earth  or  to  a  network  of  conductors  stretched  over  the  ground. 
Electric  oscillations  are  communicated  to  it  by  means  of  the 
primary  coil  to  which  it  is  directly  or  indirectly  coupled ;  the 
primary  being  included  in  an  oscillation-generating  circuit 
of  high  frequency  (Arts.  600  and  603),  containing  capacity 
and  self-induction  and  a  spark-gap  or  gaps  across  which 
sparks  at  high  voltage  are  discharged  by  the  agency  of  an 
ordinary  transformer  or  induction-coil  supplied  from  a  suit- 
able source  of  current.  In  small  installations  the  source  is  a 


a  b  c  d 

FIG.  370.  —  Various  Forms  of  Aerial  Structures  for  Radiotelegraphy. 

few  cells  of  accumulators,  where  a  town  supply  is  not  avail- 
able. In  the  great  radiotelegraphic  stations  power  is  especially 
generated  by  dynamos. 

Some  of  the  forms  of  aerial  gear  are  depicted  in  Fig.  370, 
in  which  a  is  a  capacity  area  suitable  for  stations  of  moderate 
size ;  b  and  c  are  forms  of  aerial  covering  many  hundreds  of 
square  yards  and  supported  on  masts  a  hundred  or  more  feet 
high ;  while  d  is  a  form  suitable  for  small  stations  or  for  ships. 

622.  Arrangements  of  Transmitting  Circuits.  —  There 
are  four  chief  methods  of  arranging  the  transmitting  cir- 
cuits :  (i.)  The  oscillating  system,  including  the  aerial  struc- 
ture with  its  associated  inductance-coils  and  condensers,  is 
designed  to  be  both  a  sufficiently  persistent  oscillator  and  a 
sufficiently  active  radiator  (Lodge),  (ii.)  The  transmitting 
system  consists  of  two  tuned  circuits  such  that  the  one  con- 
taining the  spark-gap  is  a  persistent  oscillator;  the  other, 
containing  the  aerial  structure,  is  a  free  radiator  maintained 


630  ELECTRICITY  AND   MAGNETISM      [PT.  n.  623 

in  oscillation  by  being  coupled  to  the  first  (Marconi), 
(iii.)  The  transmitting  system  consists  of  two  electrically 
coupled  circuits,  one  of  which,  containing  the  air-gap,  is  a 
powerful  but  not  persistent  oscillator,  being  provided  with  a 
device  for  quenching  the  spark  so  soon  as  it  has  imparted 
sufficient  energy  to  the  other  circuit  containing  the  aerial 
structure,  this  second  circuit  then  independently  radiating 
the  train  of  slightly  damped  waves  at  its  own  period  (Lodge 
and  Wien).  (iv.)  The  transmitting  system,  by  means  either 


PRIMARY 


FIG.  371.  —  Oscillations  in  a  Pair  of  Coupled  Circuits. 

of  an  oscillating  arc  (Poulsen)  or  a  high-frequency  alternator 
(Goldschmidt),  emits  a  persistent  train  of  undamped  waves 
interrupted  only  by  being  broken  up  into  long  and  short 
groups  by  the  operator's  key. 

623.  Coupling.  —  When  an  oscillation  transformer  (Tesla- 
coil  or  jigger,  Art.  603)  is  used  to  couple  together  two  circuits, 
new  complications  are  introduced  respecting  the  frequency 
(Art.  600)  of  the  oscillations ;  these  relations  being  affected 
by  the  tightness  of  the  coupling  (Art.  543).  If  the  coupling 
between  two  circuits  tuned  to  the  same  frequency  is  tight, 
then  a  phenomenon  of  periodic  exchange  of  energy  between 
the  two  circuits  is  observed,  analogous  to  the  mechanical  ex- 
change of  energy  between  two  tuned  pendulums  which  al- 


CH.  xvi.  624, 625]  RECEIVERS  631 

ternately  stop  one  another  and  start  again.  Fig.  371  illus- 
trates the  effect  which  in  each  circuit  resembles  the  acoustic 
"  beats  "  of  mistuned  organ-pipes.  In  fact,  in  each  circuit 
the  oscillation-frequency  /  is  resolved  into  two  slightly  dif- 
fering frequencies,  /i  and  /2,  which  are  related  to  one  another 
by  the  expressions  /i  =  /  -r-  V 1  -f  c,  and  /2  =  /  -f-  V 1  —  c, 
where  c  is  the  coefficient  of  coupling  (Art.  543).  If  the  coup- 
ling be  loosened  by  increasing 
the  distance  between  the  primary 
and  secondary  coils  these  inter- 
fering frequencies  die  out.  For 
this  reason,  method  (ii.)  above  is 
bad,  unless  the  coupling  is  a  loose 
one. 

624.  Quenched-Spark  and  Os- 
cillating-Arc    Systems.  —  In   the 

quenched-spark  system  (iii.)  no       FIG  372  -Oscillations  in  the 

"  /.  Quenched-Spark  System. 

difficulty  of  this  kind  occurs,  for 

the  primary  oscillations  are  quickly  damped  out,  and  only  the 
secondary  train  of  oscillations  persists,  as  illustrated  in  Fig. 
372.  The  apparatus  for  producing  the  quenched  spark  con- 
sists of  a  multiple  spark-gap  between  a  series  of  solid  copper 
disks  separated  by  very  narrow  parallel  gaps, 
giving  great  cooling-effect  (Fig.  373). 

In  Poulsen's  oscillating  arc  transmitter, 
the  arc,  formed  between  carbon  electrodes, 
immersed    in    a    hydrocarbon    vapour,    is 
FIG  373  —Multiple    snun^ed  by  a  circuit  containing  self-induc- 
Spark-GapAPPara-   tance  and  capacity  as  in  DuddelPs  singing- 
arc  experiment  (Art.  495). 

625.  Radiotelegraphic    Receivers.  —  At    the    distant    re- 
ceiving station  an  aerial  system  of  wires  is  erected  to  catch 
the  waves,  and  the  same  aerial  used  for  transmitting  can  also 
be  used  in  turn  for  receiving.     When  waves  sent  from  a  dis- 
tant station  reach  the  aerial  they  set  up  in  its  wires  oscilla- 
tions which  pass  down  through  an  oscillation  transformer  by 


632  ELECTRICITY  AND   MAGNETISM      [PT.  n.  626 

which  they  set  up  oscillations  in  a  circuit  containing  or  con- 
nected with  a  suitable  detector.  The  detector  in  turn  com- 
municates the  oscillations  to  the  relay,  or,  in  modern  practice, 
to  the  receiving  telephone.  The  circuits  of  the  receiving 
station  are  tuned  to  those  of  the  transmitting  station,  so  that 
the  receiving  instruments  shall  be  sensitive  to  waves  of  that 
particular  frequency  only  at  which  the  transmitter  is  emitting 
its  waves,  thus  excluding  as  far  as  possible  all  waves  from 
other  stations.  Tuning  is  not  necessary  for  small  installa- 
tions, though  it  is  always  advisable. 

626.  Detectors.  —  The  detector  used  in  the  first  wireless 
transmission  by  Lodge  was  a  filings  coherer  (Fig.  366),  and 
in  this  he  was  followed  by  Marconi  who  reduced  the  quantity 
and  improved  the  quality  of  the  filings :  but  filings  coherers 
are  now  obsolete.  A  much  more  certain,  but  less  sensitive 
appliance  is  Lodge's  oilwheel  coherer,  a  small  slowly  revolv- 
ing metal  wheel  the  rim  of  which  drags  its  way  through  a 
thin  oil-film  covering  a  small  pool  of  mercury.  When  elec- 
tric oscillations  are  led  to  the  wheel  they  momentarily  break 
down  the  resistance  of  the  oil  film,  and  so  permit  the  current 
from  a  single  cell  to  effect  a  signal  in  a  siphon  recorder  (Art. 
589).  Another  form  of  detector  is  electrolytic,  consisting  of 
two  microscopic  platinum  points  dipping  into  a  small  quan- 
tity of  acidulated  water.  At  the  moment  when  electric  oscil- 
lations are  led  into  it  its  conductance  is  decreased.  An  appli- 
ance of  great  certainty,  but  not  of  great  sensitiveness,  is  Mar- 
coni's variety  of  the  magnetic  detector,  wherein  the  oscillations 
are  led  through  a  small  electromagnet  magnetizing  a  travel- 
ling steel  wire,  which  in  turn  acts  inductively  on  a  telephone 
receiver.  The  crystal  detectors  now  extensively  used  consist 
of  morsels  of  zincite,  galena,  copper  pyrites,  carborundum, 
or  other  crystal  against  which  a  metal  point  or  another  crys- 
tal presses.  These  substances  possess  the  singular  property 
(Art.  432)  of  unilateral  conductivity.  When,  therefore,  os- 
cillations are  led  through  them  they  offer  more  resistance 
to  impulses  in  one  direction  than  to  those  in  the  other : 


CH.  xvi.  627,  628]    SENDING  AND    RECEIVING 


633 


Aerial 


Sending. 


Earth 


Aerial 


hence  they  deliver  in  one  direction  a  series  of  minute  currents 
which  affect  a  telephone  receiver,  so  that  the  operator  hears 
the  dot-and-dash  signals.  The  thermoelectric  cross  (Art.  479) 
can  be  used  as  a  detector  of  oscillations  in  a  similar  way. 

627.  Sending  and  Receiving.  —  Arrangements  for  sending 
and  receiving  wireless  messages  are  indicated  in  Fig.  374. 
At  the  sending  station  for  small  installations,  using  a  battery 
E  and  an  interrupter 

I  (Art.  247),  and  an 
ordinary  spark-coil 
J,  the  spark-gap  A  is 
in  the  circuit  of  the 
aerial,  an  induc- 
tance-coil L  to  re- 
duce the  frequency 
of  the  oscillations 
being  introduced  be- 
tween the  spark-gap 
and  the  lower  capac- 
ity area  or  earth ;  K 
is  the  operating  key, 
and  C  a  condenser 
shunting  the  inter- 
rupter. In  large  in- 
stallations the  pre- 
cise arrangement  of 
circuits  used  by  Tesla 
(Fig.  361)  may  be  employed;  the  aerial  structure  and  the 
earth  or  lower  capacity  area  being  respectively  connected  to 
the  B  terminals  of  that  figure.  At  the  receiving  station  Ci 
and  G£  are  adjustable  condensers,  P  and  S,  the  primary  and 
secondary  of  an  oscillation  transformer ;  LI  and  L2  are  tun- 
ing inductance  coils.  D  is  the  crystal  detector,  C  a  blocking 
condenser,  and  T  the  receiving  telephone. 

628.  Wireless  Telephony.  —  If  transmitters  of  class  iv. 
(Art.  622)  are  employed,  which  emit  continuous  trains  of 


Receiving. 

Earth 

FIG.  374.  —  Tuned  Circuits  for  Radiotelegraphy. 


634  ELECTRICITY  AND   MAGNETISM      [PT.  n.  629 

waves  with  a  frequency  of  4000  or  more  periods  per  second, 
telephonic  speech  can  be  transmitted  by  substituting  for  the 
operating  key  a  special  microphone  capable  of  carrying  several 
amperes.  The  microphone  carves  the  transmitted  current 
(and  therefore  carves  the  train  of  emitted  waves)  into  groups 
of  amplitudes  varying  in  correspondence  with  the  sounds 
spoken  into  the  microphone.  The  ordinary  telephonic  re- 
ceiver, arranged  as  in  Fig.  374,  receives  the  messages. 

629.  Other  Suggestions  for  Telegraphing  without  Wires. 
—  Morse  in  1842,  and  Lindsay  in  1854,  proposed  to  transmit 
signals  through  earth  or  water  without  direct  communicating 
wires,  by  stray  currents  between  two  base  lines,  in  one  of 
which  the  battery  and  key  were  inserted,  while  the  receiving 
instrument  was  inserted  in  the  other.  Preece  proposed  a 
system  in  which  the  magnetic  field  created  by  the  current 
in  an  extended  circuit  induced  currents  in  a  second  extended 
circuit  at  some  distance  from  the  first.  Lodge  improved 
this  plan  by  tuning  the  circuits  together.  None  of  these 
proposals  has  proved  hitherto  of  practical  importance. 


CHAPTER  XVII 

ELECTRON   THEORY   OF   ELECTRICITY 

LESSON  LXIL — Electrons  and  Ions 

630.  The  Electron.  —  It  has  been  stated  in  various  pas- 
sages (Arts.  256,  343,  and  570)  in  these  Lessons  that  elec- 
tricity apparently  exists  in  discrete  atomic  quantities  of 
a  very  minute  but  invariable  magnitude.  In  electrolysis 
each  individual  ion  is  charged,  according  to  its  valency, 
with  one,  or  two,  or  three  such  atomic  charges.  In  the  phe- 
nomena of  discharge  in  the  vacuum  tube  we  find  kathode 
"  rays  "  which  apparently  consist  of  flights  of  electric  parti- 
cles or  corpuscles  travelling  with  enormous  speeds.  Their 
electricity  is  negative,  and  their  respective  charges  are  all 
equal.  There  is  good  evidence  that  the  single  atomic  charge 
of  a  negative  ion  in  electrolysis  is  identical  with  that  of  one 
of  the  kathodic  corpuscles,  and  that  no  smaller  quantity  of 
electricity  can  exist. 

The  name  electron  was  given  by  Johnstone  Stoney  in  1891 
to  the  atomic  quantum  of  electricity ;  the  smallest  quantity 
which  can  be  transferred  from  one  atom  of  matter  to  another ; 
the  smallest  quantity  of  electricity  that  is  capable  of  existing 
alone.  The  electron  is  negative ;  that  is,  it  consists  of  nega- 
tive electricity.  If  positive  electricity  is  atomic  at  all,  its 
atom  is  a  quantity  some  thousands  of  times  greater  than  the 
atomic  quantity  of  negative  electricity.  While  the  electron 
can  exist  either  free,  or  in  association  with  atoms  or  mole- 
cules of  matter,  the  positive  atom  of  electricity  is  unknown 
in  the  free  state,  and  apparently  exists  only  as  combined  or 
associated  with  atoms  of  matter. 

635 


636  ELECTRICITY  AND   MAGNETISM     [PT.  n.  630 

The  numerical  estimates  of  the  quantity  of  electricity 
in  an  electron  vary,  since  different  methods  of  determining 
the  amount  have  yielded  slightly  differing  results.  These 
estimates  at  the  present  date  are  comprised  between  the 
following  limits : 

f  1  electron  =  1-03  X  1(T19  coulomb, 
1  1  electron  =  T6    X  KT19  coulomb. 
Or 

I  1  coulomb  =9-7    X  1018  electrons, 
1  1  coulomb  =  6-24  X  1018  electrons. 

Since  1  coulomb  (see  Art.  381)  equals  3  X  109  electrostatic 
C.G.S.  units,  the  corresponding  estimates  may  be  expressed 
as  — 

I  1  electron  =  34  X  KT10  electrostatic  C.G.S.  unit, 
1  1  electron  =  4-8  X  10~10  electrostatic  C.G.S.  unit. 

Electrons  apparently  possess  mass  (see  Art.  639).  The 
numerical  estimates  vary  between  the  following  limits : 

f  The  mass  of  1  electron  =  6-1  X  10~28  gramme, 
(  The  mass  of  1  electron  =  74  X  10~28  gramme. 

The  estimated  size  of  the  electron,  assuming  it  to  be 
spherical,  is  that  its  radius  =  1*5  X  10~13  centimetre. 

Let  us  compare  these  figures  with  those  of  a  hydrogen 
atom. 

|  The  mass  of  1  hydrogen  atom  =  1-3       X  10~24  gramme, 
\  The  mass  of  1  hydrogen  atom  =  1  -735  X  10~24  gramme. 

The  estimated  size  of  the  molecule  of  hydrogen,  'assuming 
it  to  be  spherical,  is  that  its  radius  =  2-17  X  10~8  centimetre. 

Comparing  these  values  we  see  that  an  atom  of  hydrogen 
(the  lightest  of  known  elements)  is  from  1756  to  2844  times 
as  massive  as  an  electron ;  and  that  the  size  of  the  molecule 
of  hydrogen  is  some  140,000  times  as  great  as  that  of  an 
electron. 


CH.  xvn.  631]    THE   IONS  OF  ELECTROLYSIS  637 

Electrons  are  therefore  far  smaller  than  any  of  the  atoms  of 
matter ;  and  they  differ  from  them  in  the  respect  that  while  all 
atoms  of  matter  mutually  attract  one  another  by  the  universal 
law  of  gravitation,  the  electrons  mutually  repel  one  another : 
this  repulsion  of  electrons  being  for  equal  distances  enormously 
greater  than  the  gravitational  attraction  between  atoms. 

631.  The  Ions  of  Electrolysis.  —  The  ions  concerned  in 
electrolysis  (see  Arts.  670  and  671)  are  atoms  or  groups  of 
atoms  carrying  electrons.  A  monovalent  negative  ion  (an 
anion)  is  one  which  in  being  split  off  from  a  neutral  molecule 
has  one  electron  in  excess ;  and  by  virtue  of  this  negative 
charge  moves,  when  subjected  to  an  electric  field,  towards 
the  anode.  A  monovalent  positive  ion  (a  kation)  is  one 
which  in  being  split  off  from  a  neutral  molecule  has  one  elec- 
tron too  few  to  neutralize  its  positive  electricity,  and  is  there- 
fore positive,  and  when  subjected  to  an  electric  field  moves 
towards  the  kathode.  In  an  electrolytic  cell  there  are  two 
processions  of  ions  travelling  in  opposite  directions.  When 
an  anion  such  as  a  chlorine  ion  reaches  a  soluble  anode 
such  as  zinc,  it  enters  into  combination  with  an  equivalent 
portion  of  the  zinc  (two  chlorine  atoms  to  one  zinc,  since 
zinc  is  divalent)  and  gives  its  electron  or  electrons  (in  this  case 
two)  to  the  zinc.  When  a  kation  such  as  hydrogen  reaches 
a  kathode  such  as  copper  or  platinum,  it  usually  pairs  off  with 
another  hydrogen  ion  to  form  a  molecule,  and  takes  up  one 
electron  from  the  kathode,  thereby  imparting  an  equal  posi- 
tive charge  to  the  kathode.  In  all  chemical  combinations 
or  decompositions  each  "  bond  "  or  "  valency  "  corresponds 
to  one  electron.  Electrons  must  be  capable  of  individual 
existence  at  the  moment  when  they  are  transferred  from  the 
ions  to  the  electrodes  (or  vice  versa) ;  hence  they  are  regarded 
as  continuing,  as  individuals,  all  through  the  circuit  along 
which  they  move.  A  "  current  "  of  electricity  is  therefore 
regarded  as  a  stream  of  electrons  flowing  along  the  conductor. 
Metal  wires  must  therefore  be  regarded  as  permitting  elec- 
trons to  pass  freely  between  their  molecules. 


638  ELECTRICITY  AND   MAGNETISM      [PT.  n.  632 

The  quantity  of  electricity  in  the  ionic  charge  of  a  hydrogen 
atom  may  be  reckoned  as  follows :  According  to  the  best 
estimates  in  the  theory  of  gases  a  cubic  centimetre  of  gas 
at  normal  pressure  and  temperature  contains  2-75  X  1019 
molecules,  or  5-5  X  1019  atoms;  hydrogen  being  a  diatomic 
gas.  Experiment  shows  that  1  litre  of  hydrogen  (normal) 
weighs  0-08987  gramme :  or  1  cubic  centimetre  of  hydrogen 
weighs  8-987  x  10~5  gramme.  If  5-5  X  1019  atoms  weigh 
8-987  X  10~5  gramme,  it  follows  that  1  atom  of  hydrogen 
weighs  1-64  X  10~24  gramme.  Experiment  shows  that  to 
produce  by  electrolysis  one  gramme-equivalent,  viz.  1-008 
grammes  of  hydrogen,  requires  96,550  coulombs  (Art.  256). 
Hence  to  electrolyse  1  gramme  of  hydrogen  requires  95,790 
coulombs,  so  that  the  quantity  of  the  ionic  charge  of  1  atom 
of  hydrogen  will  be  95,790  X  1-64  X  10~24  =  1-57  X  10~19 
coulomb.  The  value  of  the  electron  so  calculated  may  be 
compared  with  those  stated  above  (Art.  630).  It  falls  be- 
tween the  values  there  given. 

632.  lonization.  —  In  Art.  570  the  view  was  stated  that 
when  a  salt  (or  acid)  is  dissolved  in  water  the  solvent  itself 
produces  a  more  or  less  complete  ionization  of  the  salt. 
But  ionization  may  be  produced  by  other  means,  in  gases, 
and  even  in  solids.  Any  gas  may  be  rendered  conductive 
by  an  electric  discharge  passed  through  any  part  of  the  con- 
taining vessel.  Flames  contain  ionized  gases,  as  do  the  gas- 
eous products  of  combustion.  Hot  bodies  emit  electrons  and 
ionize  the  neighbouring  air.  At  a  dull  red  heat  a  metal  ball 
(Art.  334),  emits  positive  ions  and  can  become  negatively 
charged,  but  at  a  white  heat  it  emits  electrons  also  and 
cannot  be  charged  at  all.  Hot  platinum  wires  emit  electrons ; 
and  certain  refractory  oxides,  lime,  and  baryta  emit  electrons 
copiously  when  heated  white  hot.  In  the  newest  form  of 
Roentgen-ray  tube,  designed  by  Coolidge,  the  kathode  is  an 
incandescent  flat  spiral  of  tungsten  wire.  Light,  especially 
ultra-violet  light,  falling  on  soft  metals,  causes  them  to  throw 
off  electrons.  The  Roentgen  rays  (Art.  352)  striking  on 


CH.  xvn.  633]          CONDUCTION   IN   GASES  639 

bodies  causes  them  to  emit  electrons.  The  several  rays 
given  out  by  radium  (Art.  638),  are  capable  of  ionizing  bodies 
on  which  they  fall,  including  air.  Mere  impact  of  bodies  on 
one  another  causes  ionization ;  for  example,  air  near  a  water- 
fall is  found  to  be  ionized.  Even  ordinary  air  —  probably 
as  the  result  of  exposure  to  light  —  is  slightly  ionized  :  for  it  is 
found  impossible  to  keep  an  insulated  conductor  charged  if 
exposed  to  the  air.  Its  charge  slowly  disappears;  a  result 
formerly  attributed  to  moisture  or  dust. 

633.  Conduction  in  Gases.  —  We  may  now  apply  some  of 
these  views  to  elucidate  the  conduction  of  electricity  in  gases. 
If  a  layer  of  gas  is  bounded  by  two  parallel  plates  at  a  distance 
of  I  centimetres  apart,  between  which  there  is  maintained  a 
difference  of  potential  of  V  volts,  the  potential  gradient 
between  them  is  V//  volts  per  centimetre.  Any  ion  in  this 
electric  field  will  be  driven  along  this  field  in  proportion  to  the 
gradient  of  the  field  and  to  the  charge  on  the  ion.  There 
will  therefore  be  a  current  between  the  plates  proportional  to 
the  number  of  ions  in  the  field.  If,  therefore,  the  gas  is  ex- 
posed to  the  action  of  any  ionizing  rays,  it  will  conduct.  But 
if  the  electric  field  is  gradually  increased  in  intensity,  the 
current  is  found  not  to  increase  proportionally,  but  only  up  to 
a  certain  '  saturation  '  value,  because  as  the  proportion  of 
ions,  positive  and  negative,  present  in  the  gas  rises,  they  tend 
more  and  more  to  recombine,  producing  neutral  atoms  which 
do  not  act  as  carriers.  It  is  possible  actually  to  observe  and 
count  the  number  of  ions  present  in  a  given  volume  of  gas. 
It  was  discovered  by  Mr.  C.  T.  R.  Wilson  that  ions  serve  as 
nuclei  on  which  a  droplet  of  aqueous  vapour  can  condense. 
Hence  if  moist  dustless  air  is  used,  and  is  suddenly  cooled  by 
release  of  pressure,  the  droplets  formed  on  each  ion  are 
rendered  visible  and  can  be  counted.  This  enabled  Sir 
Joseph  J.  Thomson,  in  1898,  to  make  a  first  estimate  of  the 
value  of  the  charge  on  the  gaseous  ion.  He  found  it  to  be 
2-17  X  10~19  coulomb  for  all  gases  and  for  all  methods  of 
ionizing.  The  value  is  now  known  to  be  too  high,  since  some 


640        ELECTRICITY  AND   MAGNETISM     [PT.  n.  634,  635 


droplets  contain  more  than  one  ion;  a  nearer  value  being 
1-03  X  10~19.  The  ions  in  an  ionized  gas  can  be  filtered  off 
by  passing  the  gas  through  cotton  wool. 

634.  Electric  Valves.  —  In  Art.  351  it  was  pointed  out 
that  if  funnel-like  glass   partitions  are  fixed  in  a  vacuum 

tube,  the  discharge  passes  much  more  readily 
if  the  open  mouths  of  the  funnel  face  the 
kathode  than  is  the  case  if  the  kathode  is  op- 
posite the  narrow  orifice.  Such  an  arrange- 
ment therefore  acts  as  a  sort  of  electric  valve 
that  allows  a  current  to  pass  in  one  direction 
only,  and  can  be  used  to  rectify  an  alternating 
discharge.  Also  since  a  hot  electrode  of  car- 
bon or  one  covered  with  baryta  (Art.  632) 
emits  electrons  copiously,  it  is  possible  to  make 
a  valve  of  a  vacuum  tube  in  which  one  of  the 
electrodes  is  kept  hot.  Fleming's  valve  is  of 
this  nature.  In  Lodge's  valve  (Fig.  375)  one 
electrode  is  an  aluminium  spiral  presenting 
large  surface,  while  the  other  is  a  small  alu- 
minium rod  on  a  protected  stem.  They  are  placed  in  a  glass 
bulb,  but  the  small  rod  is  withdrawn  down  a  narrow  elonga- 
tion of  the  tube.  If  the  electrons  emitted  by  a  kathode  can- 
not reach  the  anode  readily  no  appreciable  current  passes  :  so 
if  the  spiral  is  kathode  it  emits  its  electrons  laterally,  and  they 
do  not  reach  the  disk,  whereas  if  the  disk  is  kathode  it  pro- 
jects its  electrons  directly  towards  the  spiral.  Hence  the  un- 
equal conductivity  in  the  two  directions.  Mercury  arc  vac- 
uum tubes  (Art.  496)  can  also  act  as  rectifiers  or  valves. 

635.  Conduction   in   Solids.  —  In   metal   conductors   the 
carriers  of  electricity  are  supposed  to  be  electrons,  which 
move  freely  through  the  assemblages  of  molecules  of  which 
the  conductors  consist.     This  cannot  be  unless  ionization 
in  metals  in  their  natural  state  is  complete.     No  part  of  the 
conductance  of  a  metal  is  due  to  positive  atoms.     A  cubic 
centimetre  of  copper  contains  about  1  -25  X  1024  atoms,  which 


FIG.  375.  — Lodge's 
Electric  Valve. 


CH.  xvii.  636]   ELECTRONS  IN   DIELECTRICS  641 

are  constantly  exchanging  electrons  between  themselves 
millions  of  times  a  second.  Any  electric  force  applied  to  a 
metal  mass  will  tend  to  drive  the  electrons  in  the  direction 
from  negative  to  positive ;  and  the  electric  flow  in  the  ordi- 
nary positive  current  is  simply  an  electronic  current  or  pro- 
cession in  the  other  direction.  One  coulomb  consists  of  about 
8  X  1018  electrons,  and  one  ampere  is  the  electronic  procession 
which  carries  that  quantity  of  them  past  a  given  point 
in  the  circuit  in  one  second.  If  the  electromotive-force  ap- 
plied to  any  metallic  conductor  be  increased  it  will  drive  a 
proportionately  larger  number  of  electrons  through  it  in  a 
given  time :  that  is  the  fact  really  expressed  by  Ohm's  law. 
The  frequent  collisions  of  the  electrons  with  the  metal  atoms 
doubtless  account  for  the  evolution  of  heat  in  the  conductor, 
the  production  of  heat  being  the  evidence  (and  the  measure) 
of  what  we  call  the  resistance.  Moreover  the  conductance 
of  metals  for  heat  is  well  known  to  be  greatest  in  those  metals 
that  are  the  best  conductors  of  electricity ;  doubtless  because 
both  these  phenomena  are  due  to  the  motion  of  electrons. 
In  the  good  conducting  metals  the  ratio  of  their  electric  con- 
ductivity to  their  thermal  conductivity  is  between  6  and  7 
times  1010  (C.G.S.  units).  Also  when  a  stream  of  electrons 
flows  across  the  junction  surface  between  one  metal  and 
another,  a  change  of  their  velocity  takes  place,  evidencing 
itself  by  an  absorption  or  evolution  of  heat;  and  this  is  the 
Peltier  effect  (Art.  472).  If  such  a  junction  be  heated,  the 
metals  will  deliver  their  electrons  to  one  another  at  different 
rates,  thereby  setting  up  an  electromotive-force  from  one 
metal  to  the  other ;  and  this  is  the  Seebeck  effect  (Art.  471). 
636.  Electrons  in  Dielectrics.  —  Bodies  which  do  not 
conduct  have  no  free  ions,  and  no  free  electrons  in  them. 
Pure  water  does  not  sensibly  conduct :  there  are  no  ions  in  it. 
Such  dielectrics  as  glass,  india-rubber,  or  paraffin  consist 
of  large  complex  molecules  which  imprison  their  electrons, 
so  that  they  cannot  conduct,  nor  dissolve  in  water,  nor  act 
chemically  at  ordinary  temperatures.  On  the  other  hand  a 
2T 


642  ELECTRICITY  AND   MAGNETISM      [PT.  n.  637 

perfect  vacuum  does  not  conduct  because  there  are  no  elec- 
trons in  it  to  act  as  carriers.  Suppose  a  plate  of  glass  (a 
mixture  of  silicates  of  potassium,  calcium,  etc.)  to  be  placed 
in  an  electric  field  between  two  charged  tin  foil  plates,  the 
electric  forces  will  tend  to  electrolyse  the  molecules,  striving 
to  separate  them  into  kations  and  anions,  tearing  the  elec- 
trons in  the  anodic  direction,  and  driving  the  positive  groups 
in  the  kathodic  direction,  and  producing  molecular  strains. 
But  there  will  be  no  transfer  of  electrons  and  discharges  in 
the  mass.  When  the  electric  stress  is  removed  the  strain 
is  released.  The  only  actual  locomotions  of  electrons  in 
these  operations  of  charge  and  discharge  will  be  as  we  know 
already  (Art.  65),  at  the  surface,  or  in  the  wires  leading  thereto. 
If  a  layer  of  air  is  substituted,  exactly  the  same  thing  will 
occur,  provided  the  air  is  not  ionized. 

But  dielectrics  can  be  pierced  by  a  spark:  and  a  spark 
while  it  lasts  is  a  current.  If  the  potential  gradient  at 
any  point  becomes  great  enough  to  tear  a  few  electrons 
out  of  their  molecules  there  begins  a  breakdown  of  the 
material :  the  disturbance  spreads,  volatilizing  and  ionizing 
some  of  the  molecules,  so  that  conduction  along  a  limited 
track  is  suddenly  established,  and  the  electrons  rush  through 
the  disrupted  channel,  evolving  heat  and  light. 

637.  Magnetic  Forces  of  Electrons  in  Motion.  —  Elec- 
trons moving  gpre  equivalent  to  a  current,  and  therefore 
exercise  magnetic  forces.  One  ampere  is  a  current  in  which 
the  number  of  electrons  passing  per  second  is  about  8  X  1018. 
If  a  small  electrified  body  carrying  a  charge  e  is  travelling 
with  velocity  v,  and  is  at  a  distance  r  from  any  specified  point 
in  space,  the  magnetic  intensity  §  due  to  it  at  that  point  will 
be  ev  sin  0/r2,  where  0  is  the  angle  between  the  directions  of 
v  and  r ;  and  the  direction  of  that  intensity  will  be  normal 
to  the  plane  in  which  r  and  v  are.  If  an  electron  is  travelling 
around  a  circular  orbit,  it  will  act  like  a  minute  magnet. 

Since  a  uniform  magnetic  field  is  the  equivalent  of  a  con- 
tinuous procession  of  electrons  in  a  cylindrical  sheet  around 


CH.  xvii.  638]  RADIO-ACTIVITY  643 

it,  it  follows  by  the  principle  of  action  and  reaction  that  the 
operation  of  "  cutting  "  a  magnetic  field  by  a  moving  con- 
ductor is  the  equivalent  of  starting  a  procession  of  electrons 
along  that  conductor,  and  the  direction  of  that  procession 
will  reverse  if  the  direction  of  the  movement  of  the  conductor 
is  reversed. 

Hence,  around  the  line  of  motion  a  moving  electron  creates 
a  magnetic  field  of  circular  lines,  resembling  Fig.  193.  The 
generation  of  this  field  tends,  by  Lenz's  law,  to  oppose  the 
motion,  and  its  collapse,  after  the  electron  has  passed,  tends 
to  help  the  continuance  of  the  motion.  As  long  as  the 
motion  is  uniform  these  effects  balance  one  another :  but 
they  tend  to  oppose  any  change  of  speed,  in  fact  tend  to 
resist  acceleration.  This  is  a  property  precisely  akin  to  in- 
ertia, the  property  in  virtue  of  which  mass  resists  accelera- 
tion. The  apparent  mass  of  an  electron,  as  deduced  from  its 
motion,  is  about  6-5  X  10~28  gramme,  and  this  is  probably 
entirely  electromagnetic. 

If  the  velocity  of  an  electron  be  altered  then  an  electro- 
magnetic disturbance  of  the  ether  is  emitted  from  it,  depend- 
ing on  the  acceleration.  An  electron  in  uniform  revolution 
around  an  orbit  should  therefore  emit  periodic  waves.  If  a 
flying  electron  crosses  a  magnetic  field  it  is  subject  to  a  con- 
stant deflecting  force  at  right  angles  to  its  path  and  to  the 
direction  of  the  field,  and  hence  its  path  tends  to  become  a 
circle. 

638.  Radio-activity  and  Electrons.  —  In  1896,  shortly 
after  the  discovery  of  Roentgen's  rays,  M.  Henri  Becquerel 
and  the  author  of  this  book  independently  discovered  that 
some  very  similar  rays  capable  of  passing  through  black 
paper  and  of  causing  photographic  action  were  emitted  by 
certain  fluorescent  bodies,  for  example,  by  the  salts  of  ura- 
nium. Becquerel,  after  whom  these  rays  are  named,  observed 
that  metallic  uranium  was  particularly  active.  Two  years 
later  Madame  Curie  found  in  uranium  minerals  a  constitu- 
ent more  active  than  uranium  itself,  and  succeeded  in  isolat- 


644  ELECTRICITY   AND   MAGNETISM      [PT.  n.  638 

ing  this  highly  radio-active  substance,  which  she  named  as 
radium.  Other  radio-active  substances  have  since  been  found, 
amongst  them  thorium.  Rutherford  showed  that  radium 
emits  three  kinds  of  "  rays,"  which  can  be  separated  by  pass- 
ing them  through  a  strong  magnetic  field.  They  are  also  dis- 
tinguished by  their  respective  penetrating  power,  and  differ 
in  their  properties.  Fig.  376  is  a  diagram  representing  the 
action  of  a  magnetic  field,  perpendicular  to  the  plane  of  the 
figure,  upon  the  rays  emitted  from  a  piece  of  radium  placed 
in  the  bottom  of  a  small  lead  cylinder.  They  are  known  as 
alpha,  beta,  and  gamma  rays  respectively. 
The  Alpha  rays,  which  have  small  pene- 
trating power,  are  slightly  deflected  in 
a  direction  which  shows  them  to  be 
positively  electrified,  and  they  are  now 
known  to  be  atoms,  moving  compara- 
tively slowly,  and  of  the  same  nature  as 

F,O.  376. -Emission  o'f    the  "  canal  »  wya  (Art.  344).     Thereto 

Three  Kinds  of  Rays    rays  are  corpuscular,  negatively  electri- 

from  Radium.  <?     i     i  •    i  i  j.  •  i   •  i       ,  •      i    • 

fied,  highly  penetrative,  and  identical  in 
nature  with  the  kathode  rays  (Art.  344) ,  being  flights  of  elec- 
trons. The  Gamma  rays  are  not  deflected  by  the  magnet,  are 
of  exceedingly  high  penetrating  power,  highly  ionizing,  and 
are  in  fact  identical  in  properties  with  Roentgen's  rays  (Art. 
352).  The  alpha  and  beta  rays  can  also  be  deflected  in  an 
electric  field,  while  the  gamma  rays  cannot  be.  The  gamma 
rays  travel  with  the  speed  of  light ;  the  beta  rays  at  speeds 
differing  among  themselves,  less  than  the  speed  of  light,  but 
down  to  about  one-tenth  as  great ;  while  the  alpha  particles 
travel  at  a  speed  only  about  one-twentieth  as  great.  Ruther- 
ford and  others  have  shown  that  the  radio-active  substances 
are  unstable,  giving  off  emanations  and  emitting  atoms  of 
helium  (as  alpha  particles) ,  and  thus  degenerating  at  different 
rates  through  a  series  of  transformations  in  which  they  have 
different  chemical  properties.  Radium  is  itself  a  product 
of  the  degeneration  of  uranium ;  and  it  appears  finally  to 


CH.  xvn.  639]    RATIO  OF  CHARGE   TO  MASS  645 

degenerate  into  an  inactive  product  resembling  lead.  In 
Crookes's  spinthariscope  a  minute  speck  of  radium  bromide 
shoots  off  alpha  particles,  each  of  which  on  hitting  the  surface 
of  a  phosphorescent  screen  produces  a  minute  scintillation. 

639.  Ratio  of  Charge  to  Mass.  —  Probably  the  most 
important  and  best  established  magnitude  in  this  complex 
subject  is  the  ratio  between  the  electric  charge  of  an  elec- 
tron and  its  mass.  This  ratio  was  first  ascertained  in  1897 
by  Sir  Joseph  J.  Thomson  by  a  method  which  also  determined 
the  velocity  with  which  they  move.  That  method  is  known 
as  the  method  of  crossed 
fields.  If  a  beam  of  kath- 
ode rays  in  a  vacuum 
tube  (Fig.  377)  is  sent 
between  two  adjacent 
parallel  plates  P  and  N, 
between  which  an  electric 

.  .  -  FIQ.  377.  — Experiment  of  the  Crossed  Fields. 

field  is  established  by 

connecting  them  with  a  battery  of  a  large  number  of  cells, 
the  beam  will  be  deflected  up  or  down  according  to  the  in- 
tensity of  the  electric  force.  If  the  intensity  of  the  electric 
field  be  called  X,  then  Xe  will  be  the  force  exerted  on  the 
charge  e.  If  now  there  be  applied  a  magnetic  field,  of  inten- 
sity § ,  in  a  direction  at  right  angles  to  the  beam  and  at  right 
angles  to  the  direction  of  the  electric  field,  there  will  be  a  mag- 
netic force  tending  to  deflect  the  beam  down  or  up  according 
to  the  polarity  of  the  magnetic  field.  That  force  will  be  of 
the  value  Qev,  since  ev  is  the  equivalent  of  a  current.  By 
suitably  adjusting  the  values  of  the  fields  these  two  forces 
may  be  made  to  balance  one  another  so  that  the  beam  is 
undeviated,  and  then  we  have:  Qev  =  eX;  or  v=X-r-§. 
Further,  if  the  magnetic  field  be  applied  alone,  and  is  a  uni- 
form field  over  a  considerable  area,  the  kathode  beam  will 
be  bent  into  the  arc  of  a  circle,  since  the  deflecting  force  at 
every  point  is  at  right  angles  to  the  line  of  flight  of  the  elec- 
trons. The  radius  r  of  this  curved  path  can  be  measured : 


646  ELECTRICITY  AND  MAGNETISM     IPT.  n.  639 

it  will  be  directly  proportional  to  the  velocity  of  the  electron, 
and  to  its  charge,  and  inversely  proportional  to  the  mass 

of  the  electron  and  to  the  intensity  of  the  field,  or  :  r  =  —   - 


It  follows  that  —  =  ^~.     In  Sir  Joseph  J.  Thomson's  earliest 
m        v 

experiments  he  found  the  velocity  to  be  about  one-tenth  of 

/> 

that  of  light  :  while  the  value  of  —  he  found  to  be,  in  these 

m 

first  experiments,  about  0-9  X  108  coulombs  per  gramme. 
[Subsequent  corrections  for  slow-moving  electrons  make  the 
value  1-77  X  108.]  Now  this  number  was  at  once  seen 
to  be  about  a  thousand  times  greater  than  the  number  found 
(Art.  631  above)  for  the  charged  hydrogen  ion  as  observed  in 
electrolysis,  viz.  95,790  coulombs  per  gramme.  Hence  the 
dilemma  arose  that  either  the  electrons  carried  vastly  bigger 
charges  than  the  electrolytic  hydrogen  ions  did,  or  else  the 
electrons  were  bodies  immensely  smaller  than  the  atoms  of 
hydrogen.  Thomson  chose  the  latter  alternative  and  an- 
nounced the  discovery  of  corpuscles  at  least  a  thousand  times 
smaller  than  any  known  atom.  The  value  of  the  ratio  e/m 
is  found  to  be  independent  of  the  metal  of  the  electrodes  of 
the  kathode-ray  tube,  and  of  the  residual  gas  it  contains.  It 
is  the  same,  no  matter  what  the  source  from  which  the  elec- 
trons are  obtained.  As  deduced  by  Lorentz  from  the  Zeeman 
effect  (Art.  616),  prior  to  Thomson's  determinations,  it  should 
be  1-775  X  108.  The  value  found  by  Kaufmann  from 
kathode  rays  is  1-772  X  108.  Beta  rays  from  radium  give 
1-76  X  108,  and  those  from  incandescent  lime  1-771  X  108 
coulombs  per  gramme. 

Similar  methods  applied  to  the  alpha  particles  have 
shown  that  for  them  e/m  has  a  value  of  about  4-7  X  104 
coulombs  per  gramme.  If  the  alpha  particle  is  really  a 
helium  atom,  since  helium  is  divalent  and  has  atomic  weight 
4,  the  value  of  its  e/m  should  be  half  that  of  hydrogen,  which 
is  (Art.  631)  95,790;  that  is,  it  should  be  4-78  =  104  cou- 


CH.  xvii.  640]         ELECTRONS  AND  ATOMS  647 

lombs  per  gramme.     Their  velocity  is  much  slower  than  that 
of  the  beta  particles. 

640.  Electronic  Constitution  of  Atoms. —  From  the  con- 
stancy of  the  ratio  e/m  for  electrons  from  every  source,  it 
seems  certain  that  electrons  constitute  a  definite  primordial 
substance.  From  the  circumstance  that  the  mass  of  the 
electron  appears  to  be  purely  electromagnetic,  it  has  been  in- 
ferred that  all  mass  is  also  electromagnetic ;  that  all  atoms 
are  in  fact  aggregations  of  electrons  held  together  by  a 
nucleus  of  something  that  may  be  vaguely  called  positive 
electricity,  around  which,  or  within  which,  the  electrons  are 
grouped  in  systems,  probably  revolving  around  in  orbits,  as 
in  a  sort  of  ultra-minute  solar  system.  Sir  Joseph  J.  Thom- 
son has  put  forward  many  hypotheses  as  to  such  a  possible 
constitution  of  the  atoms  of  different  elements,  but  they  can- 
not be  discussed  here.  Neither  can  the  relation  of  the  elec- 
tron to  the  ether  be  here  entered  upon. 


APPENDIX  A 


&  IN 

DEGREES 

0  IN 

RADIANS 

SINE  e 

TANGENT  6 

SOLID  ANGLE 
2  TT(!  -  cos  0) 

COMPLEMENT 

OP  6  =  <j> 

0° 

0 

0 

0 

0 

90° 

1 

•0175 

•0175 

•0175 

•000957 

89 

2 

•0349 

•0349 

•0349 

•003837 

88 

3 

•0524 

•0523 

•0524 

•00861 

87 

4 

•0698 

•0698 

•0699 

•01532 

86 

5 

•0873 

•0872 

•0875 

•02391 

85 

6 

•1047 

•1045 

•1051 

•03441 

84 

7 

•1222 

•1219 

•1228 

•04683 

83 

8 

•1396 

•1392 

•1405 

•06115 

82 

9 

•1571 

•1564 

•1584 

•07735 

81 

10 

•1745 

•1737 

•1763 

•09545 

80 

11 

•1920 

•1908 

•1944 

•1154 

79 

12 

•2094 

•2079 

•2126 

•1373 

78 

13 

•2269 

•2250 

•2309 

•1610 

77 

14 

•2444 

•2419 

•2493 

•1866 

76 

15 

•2618 

•2588 

•2680 

•2140 

75 

16 

•2793 

•2756 

•2868 

•2434 

74 

17 

•2967 

•2924 

•3057 

•2745 

73 

18 

•3142 

•3090 

•3249 

•3075 

72 

19 

•3316 

•3256 

•3443 

•3423 

71 

20 

•3491 

•3420 

•3640 

•3789 

70 

21 

•3665 

•3584 

•3839 

•4173 

69 

22 

•3840 

•3746 

•4040 

•4575 

68 

23 

•4014 

•3907 

•4245 

•4994 

67 

24 

•4189 

•4067 

•4452 

•5431 

66 

25 

•4363 

•4226 

•4663 

•5886 

65 

26 

•4538 

•4384 

•4877 

•6358 

64 

27 

•4712 

•4540 

•5095 

•6848 

63 

28 

•4887 

•4695 

•5317 

•7354 

62 

29 

•5062 

•4848 

•5543 

•7877 

61 

30 

•5236 

•5000 

•5774 

•8417 

60 

31 

•5411 

•5150 

•6009 

•8974 

59 

32 

•5585 

•5299 

•6249 

•9547 

58 

33 

•5760 

•5446 

•6494 

1-0136 

57 

34 

•5934 

•5592 

•6745 

•0741 

56 

35 

•6109 

•5736 

•7002 

•1362 

55 

36 

•6283 

•5878 

•7265 

•1999 

54 

37 

•6458 

•6018 

•7536 

•2652 

53 

38 

•6632 

•6157 

•7813 

•3319 

52 

39 

•6807 

•6293 

•8098 

•4002 

51 

40 

•6981 

•6428 

•8391 

•4700 

50 

41 

•7156 

•6561 

•8693 

•5412 

49 

42 

•7330 

•6691 

•9004 

•6138 

48 

43 

•7505 

•6820 

•9325 

•6879 

47 

44 

•7679 

•6947 

•9657 

•7634 

46 

45 

•7854 

•7071 

1-0000 

•8402 

45 

Cosine  </> 

Cotangent  $ 

27r(l-sin.<£ 

<f>  in  Degrees 

648 


ANGLES  AND  SOLID   ANGLES 


6  IN 

DEGREES 

e  IN 

RADIANS 

SINE  0 

TANGENT  0 

SOLID  ANGLE 
27r(l-cos0) 

COMPLEMENT 
OP  0  =  4> 

45° 

•7854 

•7071 

I'OOOO 

1-8402 

45° 

46 

•8029 

•7193 

1-0355 

1-9185 

44 

47 

•8203 

•7314 

1-0724 

1-9980 

43 

48 

•8378 

•7431 

1-1106 

2-0789 

42 

49 

•8552 

•7547 

1-1504 

2-1610 

41 

50     ' 

•8727 

•7660 

1-1918 

2-2444 

40 

51 

'  -8901 

•7772 

1-2349 

2-3290 

39 

52 

•9076 

•7880 

1-2799 

2-4149 

38 

53 

•9250 

•7986 

1-3270 

2-5019 

37 

54 

•9425 

•8090 

1-3764 

2-5900 

36 

55 

•9599 

•8192 

1-4282 

2-6793 

35 

56 

•9774 

•8290 

1-4826 

2-7696 

34 

57 

•9948 

•8387 

1-5399 

2-8611 

33 

58 

1-0123 

•8481 

1-6003 

2-9536 

32 

59 

1-0298 

•8572 

1-6643 

3-0472 

31 

60 

1-0472 

•8660 

1-7321 

3-1416 

30 

61 

1-0647 

•8746 

1-8041 

3-2370 

29 

62 

•0821 

•8830 

1-8807 

3-3334 

28 

63 

•0996 

•8910 

1-9626 

3-4307 

27 

64 

•1170 

•8988 

2-0503 

3-5288 

26 

65 

•1345 

•9063 

2-1445 

3-6278 

25 

66 

•1519 

•9136 

2-2460 

3-7276 

24 

67 

•1694 

•9205 

2-3559 

3-8281 

23 

68 

•1868 

•9272 

2-4751 

3-9295 

22 

69 

•2043 

•9336 

2-6051 

4-0315 

21 

70 

•2217 

•9397 

2-7475 

4-1342 

20 

71 

•2392 

•9455 

2-9042 

4-2376 

19 

72 

•2566 

•9511 

3-0777 

4-3416 

18 

73 

•2741 

•9563 

3-2709 

4-4462 

17 

74 

•2916 

•9613 

3-4874 

4-5513 

16 

75 

1-3090 

•9659 

3-7321 

4-6570 

15 

76 

1-3265 

•9703 

4-0108 

4-7632 

14 

77 

1-3439 

•9744 

4-3315 

4-8698 

13 

78 

1-3614 

•9782 

4-7046 

4-9768 

12 

79 

1-3788 

•9816 

5-1446 

5-0843 

11 

80 

1-3963 

•9848 

5-6713 

5-1921 

10 

81 

•4137 

•9877 

6-3138 

5-3003 

9 

82 

•4312 

•9903 

7-1154 

5-4087 

8 

83 

•4486 

•9926 

8-1444 

5-5174 

7 

84 

•4661 

•9945 

9-5144 

5-6264 

6 

85 

•4835 

•9962 

11-4301 

5-7356 

5 

86 

•5010 

•9976 

14-3007 

5-8449 

4 

87 

•5184 

•9986 

19-0811 

5-9543 

3 

88 

•5359 

•9994 

28-6363 

6-0639 

2 

89 

•5534 

•9999 

57-2900 

6-1735 

1 

90 

•5708 

I'OOOO 

00 

6-2832 

0 

Cosine  </> 

Cotangent  <?> 

27r(l-sin4>) 

<£  in  Degrees 

649 


APPENDIX  B 

ORDER  IN  COUNCIL  LEGALISING  DENOMINATIONS  OF  STANDARDS 
FOR  THE  MEASUREMENT  OF  ELECTRICITY  AS  BOARD  OF  TRADE 
STANDARDS 

The  Wth  day  of  January  1910 

Whereas  by  "The  Weights  and  Measures  Act,  1889,"  it  is,  among 
other  things,  enacted  that  the  Board  of  Trade  shall  from  time  to 
time  cause  such  new  denominations  of  standards  for  the  measure- 
ment of  electricity  as  appear  to  them  to  be  required  for  use  in  trade 
to  be  made  and  duly  verified. 

And  whereas  by  Order  in  Council  dated  the  23rd  day  of  August, 
1894,  Her  late  Majesty  Queen  Victoria,  by  virtue  of  the  power 
vested  in  Her  by  the  said  Act,  by  and  with  the  advice  of  Her  Privy 
Council,  was  pleased  to  approve  the  several  denominations  of 
standards  set  forth  in  the  Schedule  thereto  as  new  denominations  of 
standards  for  electrical  measurement. 

And  whereas  in  the  said  Schedule  the  limits  of  accuracy  attainable 
in  the  use  of  the  said  denominations  of  standards  are  stated  as 
follows :  — 

For  the  Ohm  within  one  hundredth  part  of  one  per  cent. 

For  the  Ampere  within  one  tenth  part  of  one  per  cent. 

For  the  Volt  within  one  tenth  part  of  one  per  cent. 

And  whereas,  at  an  International  Conference  on  Electrical  Units 
and  Standards  held  in  London  in  the  month  of  October,  1908,  the 
International  Electrical  Units  corresponding  with  the  said  denomi- 
nations of  standards  were  denned  as  follows :  — 

(1)  The  International  Ohm  is  the  resistance  offered  to  an  un- 

varying electric  current  by  a  column  of  mercury  at  the 
temperature  of  melting  ice  14-4521  grammes  in  mass  of  a 
constant  cross  sectional  area  and  of  a  length  of  106-300 
centimetres. 

(2)  The  International  Ampere  is  the  unvarying  electric  current 

which  when  passed  through  a  solution  of  nitrate  of  silver 
in  water  deposits  silver  at  the  rate  of  0-00111800  of  a 
gramme  per  second. 

650 


APPENDIX  651 

(3)  The  International  Volt  is  the  electrical  pressure  which  when 
steadily  applied  to  a  conductor  whose  resistance  is  one 
International  Ohm  will  produce  a  current  of  one  Interna- 
tional Ampere. 

And  whereas  it  has  been  made  to  appear  to  the  Board  of  Trade 
to  be  desirable  that  the  denominations  of  standards  for  the  measure- 
ment of  electricity  should  agree  in  value  with  the  said  International 
Electrical  Units  within  the  said  limits  of  accuracy  attainable. 

And  whereas  the  denominations  of  standards  made  and  duly 
verified  in  1894  and  set  forth  in  the  Schedule  to  the  said  Order  in 
Council  have  been  again  verified. 

And  whereas  the  Board  of  Trade  are  advised  that  the  said  de- 
nominations of  standards  agree  in  value  with  the  said  International 
electrical  units  within  the  said  limits  of  accuracy  attainable,  except 
that  in  the  case  of  the  Ohm  the  temperature  should  be  16-4  C.  in 
place  of  15-4  C.  as  specified  in  the  Schedule  to  the  said  Order  in 
Council. 

And  whereas  it  has  been  made  to  appear  to  the  Board  of  Trade 
that  the  said  denominations  of  standards  should  be  amended  so  that 
the  aforesaid  exception  may  be  remedied. 

Now,  therefore,  His  Majesty,  by  virtue  of  the  power  vested  in  Him 
by  the  said  Act,  by  and  with  the  advice  of  His  Privy  Council,  is 
pleased  to  revoke  the  said  Order  in  Council  dated  the  23rd  day  of 
August,  1894,  and  is  further  pleased  to  approve  the  several  denomi- 
nations of  standards  set  out  in  the  Schedule  hereto  as  denominations 
of  standards  for  the  measurement  of  electricity. 

SCHEDULE  ABOVE  KEFERRED  TO 
/.    Standard  of  Electrical  Resistance 

A  standard  of  electrical  resistance  denominated  one  Ohm  agreeing 
in  value  within  the  limits  of  accuracy  aforesaid  with  that  of  the 
International  Ohm  and  being  the  resistance  between  the  copper 
terminals  of  the  instrument  marked  "Board  of  Trade  Ohm  Standard 
Verified,  1894  and  1909,"  to  the  passage  of  an  unvarying  electrical 
current  when  the  coil  of  insulated  wire  forming  part  of  the  aforesaid 
instrument  and  connected  to  the  aforesaid  terminals  is  in  all  parts 
at  a  temperature  of  16.4  C. 

//.    Standard  of  Electrical  Current 

A  standard  of  electrical  current  denominated  one  Ampere  agreeing 
in  value  within  the  limits  of  accuracy  aforesaid  with  that  of  the 
International  Ampere  and  being  the  current  which  is  passing  in 


652  ELECTRICITY  AND  MAGNETISM 

and  through  the  coils  of  wire  forming  part  of  the  instrument  marked 
"Board  of  Trade  Ampere  Standard  Verified,  1894  amd  1909,"  when 
on  reversing  the  current  in  the  fixed  coils  the  change  in  the  forces 
acting  upon  the  suspended  coil  in  its  sighted  position  is  exactly 
balanced  by  the  force  exerted  by  Gravity  in  Westminster  upon  the 
iridioplatinum  weight  marked  A  and  forming  part  of  the  said  instru- 
ment. 

///.   Standard  of  Electrical  Pressure 

A  standard  of  electrical  pressure  denominated  one  Volt  agreeing 
in  value  within  the  limits  of  accuracy  aforesaid  with  that  of  the 
International  Volt  and  being  one  hundredth  part  of  the  pressure 
which  when  applied  between  the  terminals  forming  part  of  the  instru- 
ment marked  "Board  of  Trade  Volt  Standard  Verified,  1894  and 
1909,"  causes  that  rotation  of  the  suspended  portion  of  the  instru- 
ment which  is  exactly  measured  by  the  coincidence  of  the  sighting 
wire  with  the  image  of  the  fiducial  mark  A  before  and  after  applica- 
tion of  the  pressure  and  with  that  of  the  fiducial  mark  B  during  the 
application  of  the  pressure  these  images  being  produced  by  the  sus- 
pended mirror  and  observed  by  means  of  the  eyepiece. 

In  the  use  of  the  above  standards  the  limits  of  accuracy  attainable 
are  as  follows  :  — 

For  the  Ohm,  within  one  hundredth  part  of  one  per  cent. 

For  the  Ampere,  within  one  tenth  part  of  one  per  cent. 

For  the  Volt,  within  one  tenth  part  of  one  per  cent. 

The  coils  and  instruments  referred  to  in  this  Schedule  are  deposited 
at  the  Board  of  Trade  Standardizing  Laboratory,  8  Richmond 
Terrace,  Whitehall,  London. 


PROBLEMS  AND  EXERCISES 

QUESTIONS   ON   CHAPTER   I 

1.  In  what  respects  does  an  electrified  body  differ  from  a  non- 
electrified  body? 

2.  Name  some  of  the  different  methods  of  producing  electrifica- 
tion. 

3.  A  body  is  charged  so  feebly  that  its  electrification  will  not 
perceptibly  move  the  leaves  of  a  gold-leaf  electroscope.     Can  you 
suggest  any  means  of  ascertaining  whether  the  charge  of  the  body  is 
positive  or  negative? 

4.  How  would  you  prove  that  the  production  of  a  positive 
charge  is  accompanied  by  the  production  of  an  equal  negative 
charge  ? 

5.  Describe   an   experiment   to   prove   that   moistened   thread 
conducts  electricity  better  than  dry  thread. 

6.  Why  do  we  regard  the  two  electric  charges  produced  simul- 
taneously by  rubbing  two  bodies  together  as  being  of  opposite  kinds  ? 

7.  Explain  the  action  of  the  electrophorus.     Can  you  suggest 
any  means  for  accomplishing  by  a  rotatory  motion  the  operations  of 
lifting  up  and  down  the  cover  of  the  instrument  so  as  to  obtain  a 
continuous  supply  instead  of  an  intermittent  one? 

8.  Describe  the  state  of  the  medium  between  two   oppositely 
charged  bodies,  and  state  how  you  would  determine  the  direction 
of  the  lines  of  force  at  any  point. 

9.  Explain  the  Torsion  Balance,  and  how  it  can  be   used  to 
investigate  the  laws  of  the  distribution  of  electricity. 

10.  Describe    what    takes    place    as    an    electrified    conducting 
ball  is  made  to  approach  a  large  conducting  surface.     Show  by  a 
diagram  the  direction  and  relative  number  of  the  lines  of  force. 

11.  Two  small  balls  are  charged  respectively  with    +  24  and 
—  8  units  of  electricity.     With  what  force  will  they  attract  one 
another  when  placed  at  a  distance  of  4  centimetres  from  one  an- 
other? Ans.  12  dynes. 


654  ELECTRICITY  AND  MAGNETISM 

12.  If  these  two  balls  are  then  made  to  touch  for  an  instant 
and  then  put  back  in  their  former  positions,  with  what  force  will 
they  act  on  each  other? 

Ans.  They  will  repel  one  another  with  a  force  of  4  dynes. 

13.  Enumerate   the   essential   parts   of   an   influence   machine; 
and  explain  how  they  operate  to  produce  electrification. 

14.  Take   the   diagrammatic   representation  of   the  Wimshurst 
machine  (Fig.  39)  and  fill  in  the  lines  of  electric  force,  showing 
their  direction  and  relative  number. 

15.  Explain  the  action  of  the  Leyden  jar  by  the  consideration 
of  electric  displacement. 

16.  Describe  four  different  ways  of  electrifying  a  tourmaline 
crystal. 

17.  Zinc  filings  are  sifted  through  a  sieve  made  of  copper  wire 
upon  an  insulated  zinc  plate  joined  by  a  wire  to  an  electroscope. 
What  will  be  observed  ? 

18.  Explain  the  principle  of  an  air-condenser;  and  state  why  it  is 
that  the  two  oppositely  charged  plates  show  less  signs  of  electri- 
fication when  placed  near  together  than  when  drawn  apart  from 
one  another. 

19.  There  are  four  Leyden  jars  A,  B,  C,  and  D,  of  which  A, 
B,  and  D  are  of  glass,  C  of  gutta-percha.     A,  B,  and  C  are  of  the 
same  size,  D  being  just  twice  as  tall  and  twice  as  wide  as  the  others. 
A,  C,  and  D  are  of  the  same  thickness  of  material,  but  B  is  made  of 
glass  only  half  as  thick  as  A  or  D.     Compare  their  capacities. 

Ans.  Take  capacity  of  A  as  1 ;   that  of  B  will  be  2 ;   that  of 
C  will  be  f ;  and  that  of  D  will  be  4. 

20.  How  would  you  show  that  a  bar  made  half  of  zinc  and  half 
of  copper  is  capable  of  producing  electrification? 

21.  How  would  you  prove  that  there  is  no  electrification  within 
a  closed  conductor  ? 

22.  What  prevents  the  charge  of  a  body  from  escaping  away  at 
its  surface? 

23.  Explain  the  action  of  Hamilton's  mill  (Fig.  34). 

24.  Two  brass  balls  mounted  on  glass  stems  are  placed  half 
an  inch  apart.     One  of  them  is  gradually  charged  by  a  machine 
until  a  spark  passes  between  the  two  balls.     State  exactly  what 
happened  in  the  other  brass  ball  and  in  the  intervening  air  up  to 
the  moment  of  the  appearance  of  the  spark. 


1 1  (  <  V  y 

PROBLEMS  AND   EXERCISES  655 

25.  Define  electric  density.  A  charge  of  248  units  of  electricity 
was  imparted  to  a  sphere  of  4  centimetres  radius.  What  is  the 
density  of  the  charge?  Ans.  1-23  nearly. 

QUESTIONS   ON   CHAPTER   II 

1.  A  dozen  steel  sewing-needles  are  hung  in  a  bunch  by  threads 
through  their  eyes.     How  will  they  behave  when  hung  over  the 
pole  of  a  strong  magnet? 

2.  Explain  the  operation  of  an  iron  screen  in  protecting  a  gal- 
vanometer needle  from  magnets  in  its  vicinity,  and  state  why  it  is 
not  perfectly  effectual. 

3.  Of  what  material,  and  of  what  shape,  would  you  make  a  mag- 
net which  is  required  to  preserve  its  magnetism  unaltered  for  a  very 
long  time?     Describe  the  process  of  tempering. 

4.  What  is  meant  by  the  resultant  magnetic  force  at  a  point  ? 

5.  Six  magnetized  sewing-needles  are  thrust  vertically  through 
six  little  floats  of  cork,  and  are  placed  in  a  basin  of  water  with  their 
N-pointing  poles  upwards.     How  will  they  affect  one  another,  and 
what  will  be  the  effect  of  holding  over  them  the  S-pointing  pole  of 
a  magnet? 

6.  What  distinction  do  you  draw  between  magnets  and  magnetic 
matter  ? 

7.  On  board  an  iron  ship  which  is  laying  a  submarine  telegraph 
cable  there  is  a  galvanometer  used  for  testing  the  continuity  of 
the  cable.     It  is  necessary  to  screen  the  magnetized  needle  of  the 
galvanometer  from  being  affected  by  the  magnetism  of  the  ship. 
How  can  this  be  done  ? 

8.  How  would  you  prove  two  magnets  to  be  of  equal  strength  ? 

9.  The  force  which  a  small  magnet-pole  exerts  upon  another 
small  magnet-pole  decreases  as  you  increase  the  distance  between 
them.     What  is  the  exact  law  of  the  magnetic  force,  and  how  is  it 
proved  experimentally? 

10.  Describe  the  behaviour  of  E wing's  model  of  molecular  mag- 
netism in  a  magnetic  field,  and  show  how  it  corresponds  with  the 
behaviour  of  iron  when  magnetized.     Divide  the  process  of  magnet- 
izing into  three  successive  stages. 

11.  What  force  does  a  magnet-pole,  the  strength  of  which  is 
9  units,  exert  upon  a  pole  whose  strength  is  16  units  placed  6  cen- 
timetres away  ?  Ans.  4  dynes. 


656  ELECTRICITY  AND   MAGNETISM 

12.  How  would  you  place  a  long  magnet  so  that  one  of  its  poles 
deflects  a  compass  while  the  other  does  not  affect  it  ? 

13.  Distinguish  between  the  "strength"  of  a  magnet  and  its 
"magnetic  moment." 

14.  Describe  an  instrument  for  comparing  the  relative  values 
of  magnetic  forces.     How  would  you  use  it  to  compare  the  magnetic 
moments  of  two  magnets?     If  their  distances  from  the  magne- 
tometer are  respectively  20  centimetres  and  30  centimetres,  what  is 
the  ratio  of  their  magnetic  moments?  Ans.  8  :  27. 

15.  Two  magnets  have  the  same  pole  strength,  but  one  is  twice 
as  long  as  the  other.     The  shorter  is  placed  20  centimetres  from 
a  magnetometer    (using  the   "end-on"   method);    state   at  what 
distance  the  other  must  be  placed  in  order  that  there  may  be  no 
deflexion.  Ans.  25- 198  centimetres. 

16.  Show   how    the    formula    for    the    "end-on"    magnetometer 
measurement  is  obtained,  employing  the  law  of  inverse  squares 
and  remembering  that  the  two  poles  exert  opposite  forces  upon 
the  needle,  so  that  the  force  of  the  farther  needle  must  be  sub- 
tracted from  that  of  the  nearer  one. 

17.  Show  how  the  formula  for  the   "  broadside-on "  method  is 
obtained,  employing  the  law  of  inverse  squares  and  the  parallelo- 
gram of  forces.     (N.B.  —  On  constructing  the  correct  diagram  it 
will  be  observed  that  the  actual  force  exerted  by  each  pole  acts 
along  an  oblique  line.     To  obtain  the  force  tending  to  turn  the 
needle,  the  oblique  force  must  be  resolved  into  two  components, 
one  acting  parallel  to  the  axis  of  the  magnet,  and  tending  to  turn 
the  needle,  and  the  other  acting  along  the  line  joining  the  centres 
of  the  magnet  and  the  needle.     When  the  effects  of  the  two  poles 
are  added  together,  the  two  forces  along  the  line  joining  the  centres 
will  be  found  to  neutralize  one  another.) 

18.  A  pole  of  strength  40  units  acts  with  a  force  of  32  dynes  upon 
another  pole  5  centimetres  away.     What  is  the  strength  of  that 
pole?  Ans.  20  units. 

19.  A  magnet  does  work  in  attracting  a  piece  of  iron  to  itself. 
From  whence  comes  the  energy  necessary  to  do  this  work?     What 
changes  are  there  in  the  energy  stored  in  the  magnet  when  the  iron 
is  once  more  pulled  away? 

20.  A  magnet  10  centimetres  long  produces  on  the  needle  of  a 
magnetometer  a  deflexion  of  45°  when  their  centres  are  50  centi- 
metres apart,   at  a  place  where   H  =0-18.     Find   the  magnetic 
moment  of  the  magnet,  and  the  strength  of  its  pole  if  it  is  in  the 
end-on  position.  Ans.  m  =  1102-6  and  moment  =  11026. 


PROBLEMS  AND   EXERCISES  657 

21.  Find  the  accurate  value  of  the  moment  of  a  magnet  when 
all  the  values  are  the  same  as  stated  in  the  previous  example,  except 
that  the  magnet  occupies  the  broadside-on  position.     Ans.  =  22.842. 

22.  Find  the  value  of  the  moment  of  the  magnet  situated  as  in 
the  previous  question,  using  the  approximate  formula  only,  and 
express  the  resultant  error  as  a  percentage  of  the  correct  value. 

Ans.  moment  =  22500 ;   1-5  per  cent  low. 

23.  In  comparing  together  the  magnetic  moments  of  two  mag- 
nets by  means  of  a  magnetometer,  using  the  balance  method,  their 
respective   distances    (centre   to   centre)   from   the   magnetometer 
needle  were  found  to  be  21  centimetres  and  31-5  centimetres.     What 
is  the  ratio  of  their  magnetic  moments?  Ans.  =  8 :  27. 

24.  A  thin  bar  magnet  having  a  length  of  10  centimetres  and 
a  pole-strength  of  80  units  is  placed  so  that  both  its  poles  are  10 
centimetres  distant  from  the  centre  of  a  very  short  piece  of  mag- 
netized watch-spring,  of  which  the  magnetic  moment  is  8.     Find 
the  torque  experienced  by  the  piece  of  watch-spring  (a)  when  its 
axis  of  magnetization  is  at  right  angles  to  that  of  the  bar  magnet ; 
(6)  when  its  axis  of    magnetization  is  parallel  to  that  of  the  bar 
magnet.  Ans.   (a)   6-4  dyne-centimetres;  (b)  zero. 

25.  It  is  desired  to  compare  the  magnetic  force  at  a  point  10 
centimetres  from  the  pole  of  a  magn.et  with  the  magnetic  force 
at  5  centimetres'  distance.     Describe  four  ways  of  doing  this. 

26.  Explain  the  phenomenon  of  Consequent  Poles. 

27.  In  what  direction  do  the  lines  of  magnetic  force  run  in  a 
plane  in  which  there  is  a  single  magnetic  pole?     How  would  you 
arrange  an  experiment  by  which  to  test  your  answer  ? 

28.  A  steel  bar  magnet  suspended  horizontally,  and  set  to  oscillate 
at  Bristol,  made  110  complete  oscillations  in  five  minutes;    the 
same  needle  when  set  oscillating  horizontally  at  St.  Helena  exe- 
cuted  112  complete  oscillations  in  four  minutes.     Compare  the 
horizontal  component  of  the  force  of  the  earth's  magnetism  at 
Bristol  with  that  at  St.  Helena. 

Ans.    H  at  Bristol :  H  at  St.  Helena : :  484  :  784. 

29.  Supposing  the  dip  at  Bristol  to  be  70°  and  that  at  St.  Helena 
to  be  30°,  calculate  from  the  data  of  the  preceding  question  the 
total  force  of  the  earth's  magnetism  at  St.  Helena,  that  at  Bristol 
being  taken  as  0-48  unit.  Ans.  0-307. 

30.  A   small   magnetic   needle   was   placed   magnetically   north 
of  the  middle  point  of  a  strong  bar-magnet  which  lay  (magneti- 

2u 


658  ELECTRICITY  AND  MAGNETISM 

cally)  east  and  west.  When  the  magnet  was  3  feet  away  from  the 
needle  the  deflexion  of  the  latter  was  2° :  when  moved  up  to  a  dis- 
tance of  2  feet  the  deflexion  was  6°  30' ;  and  when  only  1  foot  apart 
the  deflexion  was  43°.  Deduce  the  law  of  the  total  action  of  one 
magnet  on  another. 

31.  Describe  how  the  daily  irregularities  of  the  earth's  magnetism 
are  registered  at  different  stations  for  comparison. 


QUESTIONS   ON   CHAPTER   III 

1.  Trace   the   successive   increases   and   decreases   of   potential 
which  go  to  make  up  the  total  electromotive  force  of  a  battery 
of  three  similar  voltaic  cells,  in  series,  starting  from  the  zinc  plate 
of  the  first  cell,  and  supposing  the  plates  to  be  immersed  in  a  liquid 
which  excites  a  potential  of  2-364  volts  in  each  zinc  plate  (when 
isolated)  and  a  potential  of  1-047  in  each  copper  plate  (when  iso- 
lated). 

2.  Classify    the    different    methods    of    preventing    polarization 
in  voltaic  cells,  and  state  the  advantages  and  disadvantages  of 
using  a  strong  depolarizer,  such  as  chromic  acid. 

3.  On  what  does  the  internal  resistance  of  a  battery  depend?     Is 
there  any  way  of  diminishing  it  ? 

4.  A  current  of  10  amperes  flows  for  half  an  hour ;   find  the  total 
quantity  of  electricity  that  passes.     Also  define  the  unit  by  which 
the  quantity  is  measured.  Ans.  18,000  coulombs. 

5.  State  from  what  source  the  energy  yielded  by  a  voltaic  cell 
is  derived. 

6.  How  is  local  action  in  a  voltaic  cell  minimized  ? 

7.  Twenty-four  similar  cells  are  grouped  together  in  four  rows 
of  six  cells  each ;    compare  the  electromotive-force  and  the  resist- 
ance of  the  battery  thus  grouped,  with   the    electromotive-force 
and  the  resistance  of  a  single  cell. 

Ans.  The  E.M.F.  of  the  battery  is  six  times  that  of  one 
cell.  The  total  internal  resistance  is  one  and  a  half 
times  that  of  one  cell. 

8.  Describe  a  form  of  cell  that  could  be  used  as  a  standard  of 
E.M.F.     State  the  essential  qualities  of  such  a  cell. 

9.  A  piece  of  silk-covered  copper  wire  is  coiled  round  the  equator 
of  a  model  terrestrial  globe.     Apply  Ampere's  rule  to  determine 


PROBLEMS  AND   EXERCISES  659 

in  which  direction  a  current  must  be  sent  through  the  coil  in  order 
that  the  model  globe  may  represent  the  condition  of  the  earth 
magnetically. 

Ans.  The  current  must  flow  across  the  Atlantic  from  Africa 
to  America,  and  across  the  Pacific  from  America  toward 
India;  or,  in  other  words,  must  flow  always  from  east 
toward  west. 

10.  A  current  of  0-24  ampere  flows  through  a  circular  coil   of 
seventy-two  turns,  the   (average)  diameter  of  the  coils  being  20 
centimetres.     What  is  the  strength  of  the  magnetic  field  which  the 
current  produces  at  the  centre  of  the  coil?  Ans.  1-08. 

11.  Show  the  direction  of  the  lines  of  force  about  a  conductor 
carrying  a  current  (1)  when  the  conductor  is  straight;    (2)  when  it 
is  bent  into  the  form  of  a  ring ;    (3)  when  it  is  wound  on  a  cylinder 
many  times  round.     What  do  you  mean  by  the  direction  of  the 
lines  of  force  ? 

12.  Suppose  a  current  passing  through  the  above  coil  produced 
a  deflexion  of  35°  upon  a  small  magnetic  needle  placed  at  its  centre 
(the  plane  of  the  coils  being  in  the  magnetic  meridian),  at  a  place 
where  the  horizontal  component  of  the  earth's  magnetic  field  is 
0-23   unit.     Calculate   the   strength   of   the   current   in   amperes. 
(Art.  226.)  Ans.  0-035. 

13.  The  current  generated  by  a  dynamo-electric  machine  was 
passed  through  a  large  ring  of  stout  copper  wire,  at  the  centre 
of  which  hung  a  small  magnetic  needle  to  serve  as  a  tangent  gal- 
vanometer.    When  the  steam  engine  drove  the  armature  of  the 
generator  at  450  revolutions  per  minute  the  deflexion  of  the  needle 
was  60°.     When  the  speed  of  the  engine  was  increased  so  as  to 
produce  900  revolutions  per  minute  the  deflexion  was  74°.     Com- 
pare the  strength  of  the  currents  in  the  two  cases. 

Ans.  The  current  was  twice  as  great  as  before,  for  tan  74° 
is  almost  exactly  double  of  tan  60°. 

14.  State  a  general  law  which  will  enable  you  to  find  the  way 
in  which  the  different  parts  of  a  magnetic  system  tend  to  move. 

15.  Deduce  the  law  of  the  force  on  a  magnetic  pole  due  to  a  cur- 
rent flowing  along  a  long  straight  conductor. 

16.  Describe  four  ways  of  controlling  the  needle  of  a  galva- 
nometer. 

17.  What  is  meant  by  a  "null-method"  of  observation? 

18.  Why  is  the  needle  of  a  tangent  galvanometer  made  very 
short? 


660  ELECTRICITY   AND  MAGNETISM 

19.  You  are  supplied  with  an  ammeter  and  a  voltmeter  for  the 
purpose  of  ascertaining   the  current   supplied   to   an  electrolytic 
bath,  and  the  voltage  at  which  it  is  supplied.     Show  in  a  diagram 
how  you  would  join  them  up. 

20.  The  current  from  two  Grove's  cells  was  passed  through  a 
sine-galvanometer  to  measure  its  strength.     When  the  conduct- 
ing wires  were  of  stout  copper  wire  the  coils  had  to  be  turned  through 
70°  before  they  stood  parallel  to  the  needle.     But  when  long  thin 
wires  were  used  as  conductors  the  coils  only  required  to  be  turned 
through  9°.     Compare  the  strength  of  the  current  in  the  first 
case  with  that  in  the  second  case  when  flowing  through  the  thin 
wires  which  offered  considerable  resistance. 

Ans.  Currents  are  as  1  to  |,  or  as  6  to  1. 

21.  Suggest  a  way  of  using  a  tangent  galvanometer  as  a  sine- 
galvanometer,  and  describe  an  appropriate  way  of  marking  a  scale 
for  this  purpose. 

22.  A  plate  of  zinc  and  a  plate  of  copper  were  respectively  united 
by  copper  wires  to  the  two  terminals  of  a  galvanometer.     They 
were  then  dipped  side  by  side  into  a  glass  containing  dilute  sul- 
phuric acid.     The  galvanometer  needle  at  first  showed  a  deflexion 
of  28°,  but  five  minutes  later  the  deflexion  had  fallen  to  11°.     How 
do  you  account  for  this  falling  off  ? 

23.  Classify  liquids   according   to   their   manner   and   power   of 
conducting    electricity.     In    which    class    would    molten    pewter 
come? 

24.  Name  the  substances  produced  at  the  anode  and  kathode 
respectively  during  the  electrolysis  of  the  following  substances : 
—  Water,   dilute   sulphuric   acid,   sulphate   of  copper    (dissolved  in 
water),   hydrochloric  acid   (strong),  iodide  of  potassium   (dissolved 
in  water),  chloride  of  tin  (fused). 

25.  A  current  is  sent  through  three  electrolytic  cells,  the  first 
containing  acidulated  water,  the  second  sulphate  of  copper,  the 
third  contains  a  solution  of  silver  in  cyanide  of  potassium.     How 
much  copper  will  have  been  deposited  in  the  second  cell  while  2-  268 
grammes  of  silver  have  been  deposited  in  the  third  cell  ?     And  what 
volume  of  mixed  gases  will  have  been  given  off  at  the  same  time  in 
the  first  cell? 

Ans.  0-6837  gramme  of  copper  and  361-5  cubic  centimetres 
of  mixed  gases. 

26.  A  current  passes  by  platinum  electrodes  through  three  cells, 
the  first  containing  a  solution  of   blue  vitriol   (cupric  sulphate), 


PROBLEMS  AND   EXERCISES  661 

the  second  containing  a  solution  of  green  vitriol  (ferrous  sulphate), 
the  third  containing  a  solution  of  ferric  chloride.  State  the  amounts 
of  the  different  substances  evolved  at  each  electrode  by  the  passage 
of  1000  coulombs  of  electricity. 

Anode  0-08292  gramme  of  oxygen  gas. 


Ans.  First  Cell  ,  Kathode  0.3294  gramme  of  copper. 

„  {  Anode  0-08292  gramme  of  oxygen. 
Second  Cell  ' 


Kathode  0.2893  gramme  of  iron, 
f  Anode  0-  3675  gramme  of  chlorine. 
\  Kathode  0-1929  gramme  of  iron. 

27.  The  ends  of  a  coil  of  fine  insulated  wire  are  connected  with 
the  terminals  of  a  galvanometer  having  a  very  light  moving  part 
which  follows  variations  of  current  which  are  not  excessively  rapid. 
A  steel  bar  magnet  is  pushed  slowly  into  the  hollow  of  the  coil  and 
then  withdrawn  suddenly.     What  actions  will  be  observed  on  the 
moving  part  of  the  galvanometer?     State  and  explain  the  differ- 
ences which  would  be  observed  in  these  actions  if  the  moving  part 
of  the  galvanometer  had  a  very  slow  periodic  time  of  vibration  and 
swung  so  freely  that  it  took  a  considerable  time  to  come  to  rest. 

28.  Round  the  outside  of  a  deep  cylindrical  jar  are  coiled  two 
separate  pieces  of  fine  silk-covered  wire,  each  consisting  of  many 
turns.     The  ends  of  one  coil  are  fastened  to  a  battery,  those  of  the 
other  to  a  sensitive  galvanometer.     When  an  iron  bar  is  poked 
into  the  jar  a  momentary  current  is  observed  in  the  galvanometer 
coils,  and  when  it  is  drawn  out  another  momentary  current,  but 
in  an  opposite  direction,  is  observed.     Explain  these  observations. 

29.  A   casement   window   has   a   continuous   iron   frame.     The 
aspect  is  north,  the  hinges  being  on  the  east  side.     What  happens 
in  the  frame  when  the  window  is  opened  ? 

30.  Explain  the  construction  of  the  induction  coil.     What  are 
the  particular  uses  of  the  condenser,  the  automatic  break,  and  the 
iron  wire  core? 

31.  It  is  desired  to  measure  the  strength  of  the  field  between 
the  poles  of  an  electromagnet  which  is  excited  by  a  current  from  a 
constant  source.     How  could  you  apply  Faraday's  discovery  of 
induction-currents  to  this  purpose? 

32.  A  small  battery  was  joined  in  circuit  with  a  coil  of  fine  wire 
and  a  galvanometer,  in  which  the  circuit  was  found  to  produce  a 
steady  but  small  deflexion.     An  unmagnetized  iron  bar  was  now 
plunged  into  the  hollow  of  the  coil  and  then  withdrawn.     The 
galvanometer  needle  was  observed  to  recede  momentarily  from  its 


662  ELECTRICITY  AND   MAGNETISM 

first  position,  then  to  return  and  to  swing  beyond  it  with  a  wider 
arc  than  before,  and  finally  to  settle  down  to  its  original  deflexion. 
Explain  these  actions,  and  state  what  was  the  source  of  the  energy 
that  moved  the  needle. 

33.  A    tangent    galvanometer,    whose    "constant"    in   absolute 
units  was  0-08,  was  joined  in  circuit  with  a  battery  and  an  elec- 
trolytic cell  containing  a  solution  of  silver.     The  current  was  kept 
on  for  one  hour ;   the  deflexion  observed  at  the  beginning  was  36°, 
but  it  fell  steadily  during  the  hour  to  34°.     Supposing  the  horizontal 
component  of  the  earth's  magnetic  force  to  be  0-23,  calculate  the 
amount  of  silver  deposited  in  the  cell  during  the  hour,  the  absolute 
electro-chemical  equivalent  of  silver  being  0-011183. 

Ans.  80-9  grammes. 

34.  A  piece  of  zinc,  at  the  lower  end  of  which  a  piece  of  copper 
wire  is  fixed,  is  suspended  in  a  glass  jar  containing  a  solution  of 
acetate  of  lead.     After  a  few  hours  a  deposit  of  lead  in  a  curious 
tree-like  form  ("Arbor  Saturni")  grows  downwards  from  the  copper 
wire.     Explain  this. 

35.  Explain    the    conditions    under    which    electricity    excites 
muscular    contraction.     How    can    the   converse    phenomenon   of 
currents  of  electricity  produced  by  muscular  contraction  be  shown? 

36.  A  current  from  2  Grove  cells  in  series  is  sent  through  a 
Daniell  cell,  entering  it  at  the  copper  pole  and  leaving  it  at  the 
zinc  pole.     Show  that  in  this  case  the  potential  is  higher  at  the 
zinc  pole  than  at  the  copper  pole.     What  becomes  of  the  energy 
which  the  2  Grove  cells  are  supplying  to  the  Daniell  cell?     (See 
Art.  264.) 

37.  Show  that  if  ^  magnetic  lines  are  withdrawn  from  a  circuit 
of  resistance   R,   the   quantity  of    electricity  thereby  transferred 
around  the  circuit  (i.e.  the  time  integral  of  the  induced  current) 
will  be  Q  =  $/R.     (See  Art.  243.) 

38.  The  strength  of  the  field  between  the  poles  of  an  electro- 
magnet was  determined  by  the  following  means :  —  A  small  cir- 
cular coil,  consisting  of  40  turns  of  fine  insulated  wire,  mounted 
on  a  handle,  was  connected  to  the  terminals  of  a  long-coil  galva- 
nometer having  a  heavy  needle.    On  inverting  this  coil  suddenly,  at 
a  place  where  the  total  intensity  of  the  earth's  magnetic  force  was 
0-48  unit,  a  deflexion  of  6°  was  shown  as  the  first  swing  of  the 
galvanometer    needle.     The    sensitiveness    of    the    galvanometer 
was  then  reduced  to  T^  by  the  insertion  of  a  resistance  coil  in  the 
circuit.     The  little  coil  was  introduced  between  the  poles  of  the 


PROBLEMS  AND  EXERCISES  663 

electromagnet  and  suddenly  inverted,  when  the  first  swing  of 
the  galvanometer  needle  reached  40°.  What  was  the  strength  of 
the  field  between  the  poles?  Ans.  315-7  units. 

QUESTIONS   ON   CHAPTER   IV 

1.  Define  the  unit  of  electricity  as  derived  in  absolute  terms  from 
the  fundamental  units  of  length,  mass,  and  time. 

2.  At  what  distance  must  a  small  sphere  charged  with  28  units 
of  electricity  be  placed  from  a  second  sphere  charged  with  56  units 
in  order  to  repel  the  latter  with  a  force  of  32  dynes  ? 

Ans.  7  centimetres. 

3.  Suppose  the  distance  from  the  earth  to  the  moon  to  be  (in 
round  numbers)  383  X  108  centimetres;    and  that  the  radius  of 
the  earth  is  63  X  107  centimetres,  and  that  of  the  moon  15  X  107 
centimetres ;   and  that  both  moon  and  earth  are  charged  until  the 
surface  density  on  each  of  them  is  of  the  average  value  of  10  units 
per  square  centimetre.     Calculate  the  electrostatic  repulsion  be- 
tween the  moon  and  the  earth. 

4.  A  small  sphere  is  electrified  with  24   units   of  +  electricity. 
Calculate  the  force  with  which  it  repels   a   unit   of  +  electricity 
at  distances  of  1,  2,  3,  4,  5,  6,  8,  and  10  centimetres  respectively. 
Then  plot  out  the  "  curve  of  force"  to  scale;   measuring  the  respec- 
tive distances  along  a  line  from  left  to  right  as  so  many  centimetres 
from  a  fixed  point  as  origin ;   then  setting  out  as  vertical  ordinates 
the  amounts  you  have  calculated  for  the  corresponding  forces; 
lastly,  connecting  by  a  curved  line  the  system  of  points  thus  found. 

5.  Define  electrostatic  (or  electric)  "potential"  ;  and  calculate  (by 
the  rule  given  in  italics  in  Art.  281)  the  potential  at  a  point  A,  which 
is  at  one  corner  of  a  square  of  8  centimetres'  side,  when  at  the  other 
three  corners  B,  C,  D,  taken  in  order,  charges  of  +  16,  +34,  and 
-f-  24  units  are  respectively  placed.  Ans.  8  (very  nearly). 

6.  A  small  sphere  is  electrified  with  24  units  of   +  electricity. 
Calculate  the  potential  due  to  this  charge  at  points  1,  2,  3,  4,  5,  6,  8, 
and    10   centimetres'    distance   respectively.     Then   plot   out   the 
"curve  of  potential"  to  scale,  as  described  in  Question  4. 

7.  A  small  sphere  charged  with  100  units  of  electricity  is  dipped 
into  a  bath  of  oil  having  inductivity  2.     Find  the  force  it  would 
exert  on  a  unit  charge  5  centimetres  away.  Ans.  2  dynes. 

8.  Distinguish  between  the  surface  density  at  a  point  and  the 
potential  at  that  point  due  to  neighbouring  charges. 


664  ELECTRICITY  AND   MAGNETISM 

9.  What  are  equipotential  surfaces?     Why  is  the  surface  of  an 
insulated  conductor  an  equipotential  surface?     Is  it  always  so? 

10.  Show  that  the  capacity  of  an  isolated  sphere  in  air  of  radius 
v  has  a  capacity  equal  to  v  units.     What  is  the  electrostatic  unit 
of  capacity  ? 

11.  Why  is  the  potential  of  the  earth  due  to  charges  that  we 
produce  practically  equal  to  zero  ? 

12.  A  sphere  whose  radius  is  14  centimetres  is  charged  until 
the  surface  density  has  a  value  of  10.     What  quantity  of  electricity 
is  required  for  this?  Ans.  24,640  units   (nearly). 

13.  In  the  above  question  what  will  be  the  potential  at  the  sur- 
face of  the  sphere?     (See  Art.  290.)  Ans.  1760  (very  nearly). 

14.  In  the  case  of  Question  12,  what  will  be  the  electric  force 
at  a  point  outside  the  sphere  and  indefinitely  near  to  its  surface? 
(Art.  294.)  Ans.  125-7  (very  nearly). 

15.  Suppose  a  sphere  whose  radius  is  10  centimetres  to  be  charged 
with  6284  units  of  electricity,  and  that  it  is  then  caused  to  share 
its  charge  with  a  non-electrified  sphere  whose  radius  is  15  centi- 
metres, what  will  the  respective  charges  and  surface-densities  on 
the  two  spheres  be  when  separated  ? 

Ans.     Small  sphere,  q  =  2513-6,  p  =  2 : 

Large  sphere,  q  =  3770-4,  p  =  1-33. 

16.  A  charge  of  +  8  units  is  collected  at  a  point  20  centimetres 
distant  from  the  centre  of  a  metallic  sphere  whose  radius  is  10 
centimetres.     It  induces  a  negative  electrification  at  the  nearest 
side  of  the  sphere.     Find  a  point  inside  the  sphere  such  that  if  4 
negative  units  were  placed  there  they  would  exercise  a  potential 
on  all  external  points  exactly  equal  to  that  of  the  actual  negative 
electrification.  (See  Art.  293.) 

Ans.  The  point  must  be  on  the  line  between  the  outside 
positive  charge  and  the  centre  of  the  sphere  and  at 
5  centims.  from  the  surface. 

17.  Two  large  parallel  metal  plates  are  charged  both  positively 
but  unequally,  the  density  at  the  surface  of  A  being  +  6,  that  at 
the  surface  of  B  being  +  3.     They  are  placed  2  centimetres  apart. 
Find  the  force  with  which  a  +  unit  of  electricity  is  urged  from  A 
towards  B.     Find  also  the  work  done  by  a  +  unit  of  electricity 
in  passing  from  A  to  B. 

Ans.  Electric  force  from  A  towards  B  =  18-85  dynes; 
work  done  by  unit  in  passing  from  A  to  B  =  37-  5 
ergs. 


PROBLEMS  AND   EXERCISES  665 

18.  What  is  meant  by  the  dimensions  of  a  physical  quantity? 
Deduce  from  the  Law  of  Inverse  Squares  the  dimensions  of  the 
unit  of  electricity ;   and  show  by  this  means  that  electricity  is  not 
a  quantity  of  the  same  physical  dimensions  as  either  matter,  energy, 
or  force. 

19.  Explain   the  construction  and  principles  of  action  of   the 
quadrant  electrometer.     How  could  this  instrument  be  made  self- 
recording  ? 

20.  Describe    the    construction    of    an    electrostatic    voltmeter, 
and  state  some  of  the  advantages  that  this  instrument  possesses. 

21.  One  of  the  two  coatings  of  a  condenser  is  put  to  earth,  to 
the  other  coating  a  charge  of  5400  units  is  imparted.     It  is  found 
that   the   difference   of   potential   thereby   produced  between  the 
coatings  is  15  (electrostatic)  units.     What  was  the  capacity  of  the 
condenser?  Ans.  360. 

22.  What  is  the  meaning  of  inductivity  f     Why  does  hot  glass 
appear  to  have  a  higher  inductivity  than  cold  glass  ? 

23.  Describe  a  method  of  mapping  out  the  lines  of  force  in  an 
electrostatic  field. 

24.  Two  condensers  of  capacity  4  and  6  respectively  are  placed 
in  parallel;    and  in  series  with  them  is  placed  another  condenser 
having  a  capacity  of  5  microfarads.     Find  the  capacity  of  the  whole 
combination.  Ans.  3-3. 

25.  Compare  the  phenomenon  of  the  residual  charge  in  a  Ley- 
den  jar  with  the  phenomenon  of  polarization  in  an  electrolytic  cell. 

26.  A  condenser  was  made  of  two  flat  square  metal  plates,  the 
side  of  each  of  them  being  35  centimetres.     A  sheet  of  india-rubber 
0-4  centim.  thick  was  placed  between  them  as  a  dielectric.     The 
inductivity  of  india-rubber  being  taken  as  2-25,  calculate  the  capac- 
ity of  the  condenser.  Ans.  548-8  electrostatic  units. 

27.  Calculate    (in   electrostatic   units)    the   capacity   of   a   mile 
of  telegraph  cable,  the  core  being  a  copper  wire  of  0-18  centim. 
diameter,  surrounded  by  a  sheathing  of  gutta-percha  0-91  centim. 
thick,     [k  for  gutta-percha  =  2-46;    one  mile  =  160,933  centims.] 

Ans.  82,164  units. 

28.  A  Leyden  jar  is  made  to  share  its  charge  with  two  other  jars, 
each  of  which  is  equal  to  it  in  capacity.     Compare  the  energy  of 
the  charge  in  one  jar  with  the  energy  of  the  original  charge. 

Ans.  One  ninth  as  great. 


666  ELECTRICITY  AND   MAGNETISM 

29.  A  series  of  Ley  den  jars  of  equal  capacity  is  charged  "in 
cascade."     Compare  the  total  energy  of  the  charge  of  the  individual 
jars  thus  charged  with  that  of  a  single  jar  charged  from  the  same 
source. 

30.  Classify  the  various  modes  of  discharge,  and  state  the  condi- 
tions under  which  they  occur. 

31.  Suppose  a  condenser,  whose  capacity  is  10,000  charged  to 
potential  14,  to  be  partially  discharged  so  that  the  potential  fell 
to  5.     Calculate  the  amount  of  heat  produced  by  the  discharge,  on 
the  supposition  that  all  the  energy  of  the  spark  is  converted  into 
heat.  Ans.  0-020357  of  a  unit  of  heat. 

32.  How  do  changes  of  pressure  affect  the  passage  of  electric 
sparks  through  air? 

33.  Describe  some  of  the  properties  of  matter  in  its  ultra-gaseous 
or  radiant  state. 

34.  Why   are   telegraphic   signals   through   a   submerged   cable 
retarded  in  transmission,  and  how  can  this  retardation  be  obviated  ? 

35.  How  is  the  difference  of  potential  between  the  earth  and  the 
air  above  it  measured  ?  and  what  light  do  such  measurements  throw 
on  the  periodic  variations  in  the  electrical  state  of  the  atmosphere  ? 

36.  What  explanation  can  be  given  of  the  phenomenon  of  a 
thunderstorm  ? 

37.  What  are  the  essential  features  which  a  lightning-conductor 
must  possess  before  it  can  be  pronounced  satisfactory?     And  what 
are  the  reasons  for  insisting  on  these  points  ? 

38.  How  can  the  duration  of  an  electric  spark  be  measured  ? 


QUESTIONS   ON   CHAPTER  V 

1.  Define  magnetic  potential,  and  find  the   (magnetic)   potential 
due  to  a  bar-magnet  10  centimetres  long,  and  of  strength  80,  at  a 
point  lying  in  a  line  with  the  magnet  poles  and  6  centimetres  distant 
from  its  N-seeking  end.  Ans.  8-3. 

2.  A  N-seeking  pole  and  a  S-seeking  pole,  whose  strengths  are 
respectively  +  120  and  —  60,  are  in  a  plane  at  a  distance  of  6  centi- 
metres apart.     Find  the  point  between  them  where  the  potential 
is  =  0 ;   and  through  this  point  draw  the  curve  of  zero  potential  in 
the  plane. 


PROBLEMS  AND   EXERCISES  667 

3.  Define  "intensity  of  the  magnetic  field."     A  magnet  whose 
strength  is  270  is  placed  in  a  uniform  magnetic  field  whose  intensity 
is  0- 166.     What  are  the  forces  which  act  upon  its  poles  ? 

Ans.  +  45  dynes  and  —  45  dynes. 

4.  Define    "intensity  of    magnetization."      A    rectangular    bar 
magnet,  whose  length  was  9  centimetres,  was  magnetized  until  the 
strength  of  its  poles  was  164.     It  was  2  centimetres  broad  and  0-5 
centimetre    thick.     Supposing    it    to    be    uniformly    magnetized 
throughout  its  length,  what  is  the  intensity  of  the  magnetization  ? 

Ans.  164. 

5.  A  certain  bipolar  electric  motor  has   100  conductors   on  its 
armature,  each  carrying  10  amperes.     The  number  of  lines  of  force 
passing  through  the  armature  is  500,000.     Find  the  work  (in  ergs) 
done  in  one  revolution  of  the  armature. 

As  each  conductor  cuts  the  lines  twice  in  one  revolution  the 
answer  will  be  100,000,000  ergs. 

6.  Find  the  torque  (see  Art.  518)  on  the  armature  described  in 
the  last  question.     Note  that  with  the  above  data  the  torque  is 
independent  of  the  radius  of  the  armature,  for  the  force  on  each  con- 
ductor is  proportional  to  the  strength  of  the  field,  and  this  is  inversely 
proportional  to  the  radius  if  gf  remains  the  same. 

Ans.100'™'000  dyne-centimetre*. 

7.  A    current   whose    strength    in   "absolute"    electromagnetic 
units  was  equal  to  0-05  traversed  a  wire  ring  of  2  centimetres  radius. 
What  was  the  strength  of  field  at  the  centre  of  the  ring?     What 
was  the  potential  at  a  point  P  opposite  the  middle  of  the  ring  and 
4  centimetres  distant  from  the  circumference  of  the  ring  ? 

Ans./  =  0-1571;  V  =  ±  0-0421. 

8.  (a)  A  spiral  of  wire  of  1000  turns  80  centimetres  long  carries 
a  current  of  1  ampere.     Find  the  strength  of  the  magnetic  field  pro- 
duced at  the  middle  point  of  this  coil.  Ans.  §  =  15-71. 

(6)  If  this  spiral  were  1  metre  in  length  and  1  centimetre  in 
diameter,  find  the  force  on  a  unit  pole  placed  (1)  in  its  centre ;  (2)  at 
its  end.  Ans.  12-57  dynes  and  6-28  dynes. 

9.  What  limits  are  there  to  the  pull  of  an  electromagnet  ? 

10.  What  is  the  advantage  in  using  an  iron  core  in  an  electro- 
magnet ? 

11.  A  rod  of  soft  iron,  0-32  cm.  in  diameter  and  1  metre  long,  is 
uniformly  overwound  from  end  to  end  with  an  insulated  copper  wire 


668  ELECTRICITY  AND   MAGNETISM 

making  637  turns  in  one  layer.  Find  (using  Bidwell's  data  in  Art. 
392)  what  strength  of  poles  this  rod  will  acquire  when  a  current  of 
5  amperes  is  sent  through  the  coil.  Ans.  98-5  units. 

12.  Enunciate  Maxwell's  rule  concerning  magnetic  shells,  and 
from  it  deduce  the  laws  of  parallel  and  oblique  currents  discovered 
by  Ampere. 

13.  A  circular  copper  dish  is  joined  to  the  zinc  pole  of  a  small 
battery.     Acidulated  water  is  then  poured  into  the  dish,  and  a  wire 
from  the  carbon  pole  of  the  battery  dips  into  the  liquid  at  the  middle. 
A  few  scraps  of  cork  are  thrown  in  to  render  any  movement  of  the 
liquid  visible.     What  will  occur  when  the  N-seeking  pole  of  a  strong 
bar  magnet  is  held  above  the  dish? 

14.  Roget  hung  up  a  spiral  of  copper  wire  so  that  the  lower  end 
just  dipped  into  a  cup  of  mercury.     When  a  strong  current  was  sent 
through  the  spiral  it  started  a  continuous  dance,  the  lower  end  pro- 
ducing bright  sparks  as  it  dipped  in  and  out  of  the  mercury.     Explain 
this  experiment. 

15.  It  is  believed,  though  it  has  not  yet  been  proved,  that  ozone 
is  more  strongly  magnetic  than  oxygen.     How  could  this  be  put 
to  proof? 

16.  What  is  meant  by  the  permeability  of  a  substance?     State 
some  substances  in  which  it  is  constant,  and  some  in  which  it  varies. 

17.  Describe  a  method  of  measuring  the  permeability  of  iron. 

18.  A  ring  of  iron  is  wound  with  two  coils.     One  coil  is  connected 
to  a  ballistic  galvanometer,  and  on  connecting  the  other  to  a  battery 
a  throw  of  the  needle  of  160  scale  divisions  is  observed.     The  current 
is  then  broken  and  there  is  a  throw  of  40  divisions  in  the  opposite 
direction.     Why  are  the  two  throws  not  equal?     What  change  has 
taken  place  in  the  iron  ?     How  would  you  bring  it  back  to  its  original 
condition  ? 

19.  Sketch  a  closed  hysteresis  curve  for  hard  steel,  for  which, 
when  £  is  raised  to  100,  33  =  12,800,  and  for  which  the  remanence 
is  93  =  9500  and  the  coercive  force  40. 

20.  An  iron  bar  30  centimetres  long  and  10  square  centimetres 
in  sectional  area  is  bent  into  the  shape  of  a  horse-shoe  for  the  purpose 
of  making  an  electromagnet  which  shall  have  a  pull  of  66  kilograms 
upon  its  armature  (a  bar  12  centimetres  long  and  10  square  centi- 
metres in  section)  when  it  is  ^  inch  away  from  its  poles.     Find  the 
number  of  ampere- turns  required,  assuming  a  leakage  of  one-third 
of  the  lines  of  force. 


PROBLEMS  AND   EXERCISES  669 

Taking  the  formula  :  — 

—  X  20  sq.  cms.  of  pole  face  =  66,000  X  981  dynes, 

8  TT 

we  get  33  =  9000.  From  the  table,  Art.  391,  MI  for  the  armature 
=  2250,  23  for  the  horse-shoe  =  1-5  X  9000  =  13,500,  so  that 
/*2  =  900,  then  ampere-turns  = 

90'00°  +  +  2X°'5X2'54      *  l'»*  -18.85°. 


21.  What  thickness  of  copper  wire  must  be  used  to  wind  the  above 
magnet  in  order  to  obtain  18,650  ampere-turns,  the  winding  on  each 
cylindrical  bobbin  having  a  mean  diameter  of  7  centimetres,  if  the 
pressure  at  the  terminals  of  the  magnet  is  intended  to  be  100  volts  ? 

If  r  is  the  resistance  of  one  turn,  and  s  the  number  of  turns, 

r  =  H  =     10Q    ;  but  we  know  that  r  =  7  X  "  X  1-6  X  10'6. 
is      18,650  d2  X  \ir 


Hence  diameter  of  wire,  d  =  ^18,650  X  7  X4  X  1-6  =  Q.Q914 

centimetre. 

N.B.  —  The  thickness  of  wire  is  independent  of  the  number  of 
turns  (except  in  so  far  as  this  affects  the  mean  diameter  of  the 
bobbin),  but  the  greater  the  number  of  turns  the  less  will  be  the 
number  of  watts  expended. 

22.  What  is  the  object  of  "polarizing"  the  armature  of  a  magnet 
in  a  piece  of  mechanism,  such  as  a  relay? 

23.  Describe  the  construction  of  a  current-balance,  and  the  mode 
of  using  it. 

QUESTIONS   ON   CHAPTER   VI 

1.  The  resistance  of  telegraph  wire  being  taken  as  13  ohms  per 
mile,  and  the  E.M.F.  of  a  Leclanche  cell  as  1-4  volt,  calculate  how 
many  cells  are  needed  to  send  a  current  of  12  milli-amperes  through 
a  line  120  miles  long;    assuming  that  the  instruments  in  circuit 
offer  as  much  resistance  as  20  miles  of  wire  would  do,  and  that  the 
return  current  through  earth  meets  with  no  appreciable  resistance. 

Ans.  16  cells* 

2.  50  Grove's  cells  (E.M.F.  of  a  Grove  =1-8  volts)  are  united 
in  series,  and  the  circuit  is  completed  by  a  wire  whose  resistance  is 
15  ohms.     Supposing  the  internal  resistance  of  each  cell  to  be  0-3 
ohm,  calculate  the  strength  of  the  current.  Ans.  3  amperes. 


670  ELECTRICITY  AND   MAGNETISM 

3.  The  current  running  through  an  incandescent   filament   of 
carbon  in  a  lamp  was  found  to  be  exactly  1  ampere.     The  difference 
of  potential  between  the  two  terminals  of  the  lamp  while  the  current 
was  flowing  was  found  to  be  30  volts.     What  was  the'  resistance  of  the 
filament  ? 

4.  Define  resistivity.     Taking  the  resistivity  (Art.  435)  of  copper 
as  1-.642,  calculate  the  resistance  of  a  kilometre-of  copper  wire  whose 
diameter  is  1  millimetre.  Ans.  20-9  ohms. 

5.  On  measuring  the  resistance  of  a  piece  of  No.  30  B.W.G. 
(covered)  copper  wire,  18- 12  yards  long,  I  found  it  to  have  a  re- 
sistance of  3-02  ohms.     Another  coil  of  the  same  wire  had  a  resistance 
of  22-65  ohms;  what  length  of  wire  was  there  in  the  coil? 

Ans.  135-9  yards. 

6.  Calculate  the  resistance  at  0°  Centigrade  of  a  copper  conductor 
one  square  centimetre  in  area  of  cross-section,  and  long  enough  to 
reach  from  Niagara  to  New  York,  reckoning  this  distance  as  480 
kilometres.  Ans.  78-8  ohms. 

7.  Find  the  drop  in  volts  if  400  amperes  is  passed  through  this  con- 
ductor.    What  would  be  the  waste  of  power  (in  watts)  ? 

Ans.  31,520  volts,  12,608,000  watts. 

8.  The  resistance  from  plate  to  plate  in  a  certain  electrolytic 
bath  is  0-9  of  an  ohm.     You  wish  to  pass  through  it  the  strongest 
current  you  can  get  from  20  Daniell  cells,  each  with  a  resistance  of 
one  ohm.     How  would  you  group  the  cells? 

Ans.  4  in  series,  5  rows  in  parallel. 

9.  The  specific  resistance  of  gutta-percha  being  3-5  X  1020,  cal- 
culate the  number  of  coulombs  of  electricity  that  would  leak  in  one 
century  through  a  sheet  of  gutta-percha  one  centimetre  thick  and  one 
metre  square,  whose  faces  were  covered  with  tinfoil  and  joined 
respectively  to  the  poles  of  a  battery  of  100  Daniell's  cells. 

Ans.  9-7  coulombs. 

10.  Six  Daniell's  cells,  for  each  of  which  E  =1-05  volt,  r  =  0-5 
ohm,  are  joined  in  series.     Three  wires,  X,  Y,  and  Z,  whose  resist- 
ances are  respectively  3,  30,  and  300  ohms,  can  be  inserted  between 
the  poles  of  the  battery.     Determine  the  current  which  flows  when 
each  wire  is  inserted  separately;    also  determine  that  which  flows 
when  they  are  all  inserted  at  once  in  parallel. 

Ans.  Through  X  1-05      ampere. 

Through  Y  0-1909       " 

Through  Z  0-0207 

Through  all  three  1- 105 


PROBLEMS  AND   EXERCISES  671 

11.  Calculate  the  number  of  cells  required  to  produce  a  current 
of  50  milli-amperes,  through  a  line  114  miles  long,  whose  resistance 
is  12 1  ohms  per  mile,  the  available  cells  of  the  battery  having  each 
an  internal  resistance  of  1-5  ohm,  and  an  E.M.F.  of  1-5  volt. 

Ans.  50  cells. 

12.  You   have    20    large    Leclanche    cells     (E.M.F.  =1-5  volts, 
r  =  0-5  ohm  each)  in  a  circuit  in  which  the  external  resistance  is 
10  ohms.     Find  the  strength  of  current  which  flows  (a)  when  the 
cells  are  joined  in  simple  series ;    (6)  when  all  the  zincs  are  united, 
and  all  the  carbons  united,  in  parallel;     (c)   when   the  cells  are 
arranged  two  abreast  (i.e.  in  two  files  of  ten  cells  each) ;    (d)  when 
the  cells  are  arranged  four  abreast. 

Ans.  (a)   1-5;    (6)0-1496;    (c)l-2;    (d)  0-702  ampere. 

13.  With  the  same  battery  how  would  you  arrange  the  cells  in 
order  to  telegraph  through  a  line  100  miles  long,  reckoning  the  line 
resistance  as  12^  ohms  per  mile? 

14.  Show  that,  if  we  have  a  battery  of  n  given  cells  each  of 
resistance  r  in  a  circuit  where  the  external  resistance  is  R,  the 
strength  of  the  current  will  be  a  maximum  when  the  cells  are  coupled 
up  in  a  certain  number  of  rows  equal  numerically  to  Vnr  -r-  R. 

15.  Two  wires,  whose  separate  resistances  are  28  and  24,  are 
placed  in  parallel,  in  a  circuit  so  that  the  current    divides,  part 
passing  through  one,  part  through  the  other.     What  resistance  do 
they  offer  thus  to  the  current?  Ans.  12-92  ohms. 

16.  Using  a  large  bichromate  cell  of  practically  no  internal  resist- 
ance, a  deflexion  of  9°  was  obtained  upon  a  tangent  galvanometer 
(also  of  small  resistance)  through  a  wire  whose  resistance  was  known 
to  be  435  ohms.     The  same  cell  gave  a  deflexion  of  5°  upon  the  same 
galvanometer  when  a  wire  of  unknown  resistance  was  substituted 
in  the  circuit.     What  was  the  unknown  resistance? 

Ans.  790  ohms. 

17.  In  a  Wheatstone's  bridge  in  which  resistances  of  10  and  100 
ohms  respectively  were  used  as  the  fixed  resistances,  a  wire  whose 
resistance  was  to  be  determined  was  placed :    its  resistance  was 
balanced  when  the  adjustable  coils  were  arranged  to  throw  281  ohms 
into  circuit.     What  was  its  resistance?  Ans.  28-1  ohms. 

18.  Describe  the  method  of   using  a  metre  bridge  to  measure 
resistances. 

19.  Give  the  proof  of  Foster's  method  of  measuring  small  dif- 
ferences of  resistance,  from  the  consideration  of  Ohm's  law. 


672  ELECTRICITY  AND  MAGNETISM 

20.  To  find  the  voltage  of  a  dynamo  you  connect  to  its  brushes 
the  ends  of  a  German  silver  wire  120  feet  long,  wound  on  an  insu- 
lating cylinder,  and  find  that  when  one  terminal  of  a  Daniell  cell 
(1-05  volts)  is  joined  to  a  point  on  the  wire,  and  the  other  terminal  in 
series  with  a  galvanometer  is  connected  to  another  point  1  ft.  from 
the  first,  no  deflexion  is  observed.     What  is  the  voltage  of  the 
dynamo?  Ans.  126  volts. 

21.  A  battery  of  5  Leclanche  cells  was  connected  in  simple  circuit 
with  a  galvanometer  and  a  box  of  resistance  coils.     A  deflexion  of 
39°  having  been  obtained  by  adjustment  of  the  resistances,  it  was 
found  that  the  introduction  of  150  additional  ohms  of  resistance 
brought  down  the  deflexion  to  22°.     Assuming  the  galvanometer  to 
have  140  ohms  resistance,  find  the  internal  resistance  of  the  battery. 

Ans.  10  ohms. 

22.  How  are  standard  resistance  coils  wound,  and  why?     What 
materials  are  they  made  of,  and  why? 

23.  Three  very  small    Daniell's  cells  gave,  with  a  sine  galva- 
nometer (itself  of  no  appreciable  resistance),  a  reading  of  57°.     On 
throwing  20  ohms  into  the  circuit  the  galvanometer  reading  fell 
to  25°.     Calculate  the  internal  resistance  of  the  cells. 

Ans.  6-6  ohms  each. 

24.  A  length  of  telegraph  cable  was  plunged  in  a  tub  of  water 
and  then  charged  for  a  minute  from  a  battery  of  120  Daniell's  cells. 
The  cable  was  then  discharged  through  a  long-coil  galvanometer 
with  a  needle  of  slow  swing.    The  first  swing  was  40°.    A  condenser 
whose  capacity  was  |  microfarad  was  then  similarly  charged  and 
discharged;    but  this  time  the  first  swing  of  the  needle  was  only 
14°.     What  was  the  capacity  of  the  piece  of  cable? 

Ans.   0-934   microfarad. 

25.  Using  an  absolute  electrometer,  Lord  Kelvin  found  the  dif- 
ference of  potential  between  the  poles  of  a  Daniell's  cell  to  be 
0-00374  electrostatic  unit  (C.G.S.  system).      The  ratio  of  the  elec- 
trostatic to  the  electromagnetic  unit  of  potential  is  given  in  Art. 
386,   being     =  l/v.     The  volt  is   defined   as    108  electromagnetic 
units.      From  these  data  calculate  the  E.M.F.  of  a  Daniell's  cell 
in  volts.  Ans.    1-115   volts. 

26.  The  radius  of  the  earth  is  approximately  63  X  107  centi- 
metres.    The   ratio   of   the   electrostatic   to    the   electromagnetic 
unit  of  capacity  is  given  in  Art.  386.     The  definition  of  the  farad 
is  given  in  Art.  381.     Calculate  the  capacity  of  the  earth  (regarded 
as  a  sphere)  in  microfarads.  Ans.  700  microfarads  (nearly). 


PROBLEMS  AND   EXERCISES  673 

27.  The  electromotive-force  of  a  Daniell's  cell  was  determined 
by  the  following  process :  —  Five  newly  prepared  cells  were  set 
up  in  series  with  a  tangent  galvanometer,  whose    constants  were 
found  by  measurement.     The  resistances  of  the  circuit  were  also 
measured,  and  found  to  be  in  total  16-9  ohms.     Knowing  the  resist- 
ance and  the  absolute  strength  of    current    the  E.M.F.  could    be 
calculated.     The  deflexion  obtained  was  45°,  the  number  of  turns 
of  wire  in  the  coil  10,  the  average  radius  of  the  coils  11  centimetres, 
and  the  value  of  the  horizontal  component  of  the  earth's  magnetism 
at  the  place  was  0-18  C.G.S.   unit.      Deduce  the  E.M.F.   of    a 
Daniell's  cell.         Ans.  1-0647  X  108  C.G.S.  units,  or  1-0647  volts. 

28.  Apply  the  formula  of  the  ballistic  galvanometer  (Art.  451,  6) 
to  determine  the  number  of  magnetic  lines  cut  by  an  exploring 
coil  (Art.  393,  6)  when  the  magnetism  in  the  core  on  which  it  is 
wound  is  suddenly  reversed.     If  R  is  the  resistance  of  the  circuit, 
Q  =  2  $/R.      Hence  the  answer  is  ft  =  RT  sin  fa/2  TrS,  where  S 
is  the  number  of  turns  in  the  exploring-coil. 

29.  Suppose  a  copper  disk  to  revolve  in  a  field  produced  by  a 
fixed  coil  closely  surrounding  its  circumference.     In  circuit  with 
the  coil  is  a  small  battery  and  a  resistance  wire.     In  the  wire  are 
found  two  points  such  that  the  fall  of  potential  between  them  is 
equal  to  the  volts  generated  between  the  centre  and  circumference 
of  the  revolving  disk.     By  balancing  these  with  a  galvanometer 
Lorenz  was  able  to  calculate  in  absolute  measure  the  resistance  of 
the  wire.     If  M  be  the  coefficient  of  mutual  induction  between  the 
circumference  of  the  disk  and  the  surrounding  coil,  and  T  the  period 
of  revolution  of  the  disk,  show  that  R  the  resistance  between  the 
points  =  M  -s-  T. 

Ans.  Since  ^  the  magnetic  flux  through  the  disk  =  Mi,  and 
E  =  ft/T,  and  i  =  E/R,  it  follows  that  iR  =  Mi/T, 
whence  R  =  M/T.  Q.E.D. 

30.  A  certain  motor  has  a  resistance  of  0-25  of  an  ohm.     (a) 
Find  the  value  of  a  starting  resistance  such  that  it  will  limit  the 
starting  current  to  10  amperes  when  the  supply  voltage  is  100. 

Find  the  value  which  the  starting  current  would  have  if  the 
full  voltage  were  applied  to  the  armature  without  any  starting 
resistance.  Ans.  (a)  9-75  ohms. 

(6)  400  amperes. 

31.  An   unloaded   electric   motor  runs   at   500   revolutions   per 
minute  and  exerts  a  back  electromotive-force  of  98-5  when  con- 
nected to  supply  mains  at  100  volts.     The  resistance  of  the  arma- 
ture from  brush  to  brush  is  0-75  of  an  ohm. 

2x 


674  ELECTRICITY  AND  MAGNETISM 

(a)  Find  the  current  taken  by  the  armature. 

(6)  Find  the  current  taken  by  the  armature  when  mechanically 
loaded  by  a  pump  which  reduces  its  speed  to  480  revolutions  per 
minute. 

Assume  that  the  back  electromotive-force  of  the  armature  is 
directly  proportional  to  the  speed.  Ans.  (a)  Current  =  2  amperes. 

(6)  Current  =  7-33. 

32.  In   order   to   measure   the   brush-to-brush   resistance    of   a 
certain  dynamo  armature  it  is  connected  in  circuit  with  an  accumu- 
lator cell  and  an  amperemeter  which  shows  the  current  to  be  40 
amperes.     A  voltmeter  connected  to  the  two  brushes  indicates  a 
difference  of  potential  of  1  -9  volt. 

Calculate  the  resistance  of  the  armature. 

Ans.  0-475  of  an  ohm. 

33.  A  test  similar  to  that  described  in  the  preceding  example 
is  arranged  for  measuring  the  resistance  of  a  small  lamp,  the  same 
accumulator  being  employed.     The  voltmeter  reads  2  volts,  but 
the  current  is  found  to  be  only  0-25  of  an  ampere. 

On  substituting  another  voltmeter  the  current  changes  to  0-24 
of  an  ampere. 

Explain  (a)  the  increase  of  the  voltmeter  reading  above  the 
value  measured  in  the  preceding  test,  (b)  the  decrease  of  current 
produced  by  the  substitution  of  a  second  voltmeter,  (c)  Also  sug- 
gest a  test  which,  without  the  use  of  additional  apparatus,  would 
enable  you  to  obtain  a  reasonably  accurate  result  with  any  suitable 
and  correctly  calibrated  voltmeter.  Would  this  additional  test  be 
equally  necessary  in  the  preceding  example  ? 

34.  A  current  of  30  amperes  at  100  volts  is  required  to  light 
a  certain  building  and  is  supplied  through  a  pair  of  mains  which 
has  a  total  resistance  of  a  tenth  of  an  ohm.     Find  the  voltage  at 
the  terminals  of  the  dynamo  which  supplies  the  mains.      Ans.  103. 

35.  A  certain  building  requires  a  current  of  40  amperes  at  200 
volts,  and  is  supplied  by  a  dynamo  500  yards  distant. 

The  total  fall  of  potential  in  the  two  mains  must  not  exceed  4  per 
cent  of  the  voltage  in  the  building. 

Find  the  cross-section  of  the  copper  mains  if  their  temperature  is 
20°  Centigrade. 

Assume  that  the  resistivity  of  copper  is  0-64  microhm  for  an 
inch  cube  and  that  its  resistance  rises  0-4  per  cent  for  every  degree 
of  temperature  rise  above  0°  Centigrade.  Ans.  0-1244. 


PROBLEMS  AND   EXERCISES  675 

36.  Fall  of  potential  takes  place  in  the  resistance  of  generators 
and  follows  the  same  laws  as  for  any  other  resistances.     A  prim- 
ary cell  having  an  electromotive-force  of  2  volts  and  an  internal 
resistance  of  0-25  of  an  ohm  is  inserted  successively  in  two  circuits 
in  which  it  produces  currents  of  one  and  two  amperes. 

In  both  cases  find  the  potential  difference  at  the  terminals  of 
the  cell.  Ans.  1-75  volt  at  1  ampere. 

1-5  volt  at  2  amperes. 

37.  A  certain  dynamo  has  a  resistance  of  0-4  of  an  ohm  from 
brush  to  brush  and  is  driven  at  such  speed  that  its  electromotive- 
force  is  500  volts. 

When  it  supplies  a  circuit  which  takes  a  current  of  10  amperes 
what  will  be  the  reading  of  a  voltmeter  connected  across  the  brushes  ? 
It  is  assumed  that  the  electromotive-force  is  constant. 

Ans.  Voltage  =  496. 

38.  Two  different  voltmeters  read  the  same  value  when  used 
for   testing   the   electromotive-force   of  an  accumulator  cell,   but 
read  different  values  when  used  for  testing  that  of  a  Leclanche 
cell. 

Under  suspicion  that  their  scales  are  not  accurately  marked, 
they  are  subsequently  connected  in  parallel  across  the  Leclanche 
cell  with  a  view  to  comparison. 

It  is  found  that  their  readings  are  now  identical,  but  are  lower 
than  either  of  the  readings  obtained  when  they  were  employed 
separately. 

Explain  these  facts. 

39.  A   certain   old-fashioned   but   accurate   voltmeter   is   found 
to  take  a  current  of  0-2  of  an  ampere  when  connected  to  supply- 
mains   at   100  volts.     The   same   supply-mains  are   subsequently 
connected   through   an  amperemeter   to   a   glow-lamp  across    the 
terminals  of  which  the  same  voltmeter  is  connected. 

The  supply  voltage  having  in  the  meantime  risen  slightly  it  is 
found  that  the  voltmeter  reads  105  volts,  while  the  amperemeter 
reads  0-6  of  an  ampere. 

Calculate  the  exact  value  of  the  resistance  of  the  glow-lamp 
when  burning  under  these  conditions.  Ans.  269.-2  ohms. 

40.  Show  from  the  definitions  of  the  horse-power  and  of  the 
watt,  and  from  the  relations  between  the  pound  and  the  gramme, 
the  foot  and  the  centimetre,  that  there  are  746  watts  in  one  horse- 
power. 


676  ELECTRICITY  AND  MAGNETISM 

41.  Describe    the    construction   of   a    wattmeter   and    explain 
how  you  would  connect  it  up  to  measure  the  power  supplied  to  an 
electric  motor. 

42.  Mention  some  of  the  principles  upon  which  supply  meters 
have  been  designed. 

QUESTIONS   ON   CHAPTER   VII 

1.  Calculate  by  Joule's  law  the  number  of  calories  developed 
in  a  wire  whose  resistance  is  4  ohms  when  a  steady  current  of  0-14 
ampere  is  passed  through  it  for  ten  minutes.        Ans.    11-2   calories. 

2.  Why  does  a  long  thin  platinum  wire,  when  a  steady  voltage 
is  applied  to  it,  rise  to  a  certain  temperature  and  then  remain  at 
that  temperature  without  alteration? 

3.  Explain  why  you  would  expect  the  heat  produced  in  a  con- 
ductor to  be  proportional  to  the  square  of  the  current. 

4.  The  exciting  winding  of  a  certain  generator  has  a  resistance 
of  50  ohms  and  is  at  its  working  temperature  energized  from  mains 
at  100  volts. 

(a)  Without  calculating  the  current  write  down  the  value  of  the 
power  absorbed  by  this  winding. 

(6)  Find  the  number  of  calories  of  heat  per  minute  dissipated 
from  it  when  it  has  reached  a  constant  temperature. 

Ans.   (a)  200  watts. 

(6)  2857  calories. 

5.  Give  two  or  three  examples  of  appliances  in  which  i2R  repre- 
sents the  whole  power  supplied  and  utilized  by  the  appliance,  and 
also  two  or  three  in  which  i2R  only  represents  a  wasted  fraction  of 
the  whole  power  supplied  to  the  appliances. 

6.  An  electric  kettle  holding  1  quart  of  water  takes  five  minutes 
to  raise  the  temperature  from  95°  Fahrenheit  to  boiling  point. 
The  supply  voltage  is  200  and  the  cost  of  electrical  energy  is  3d. 
per  kilowatt  hour.     Under  these  conditions  the  efficiency  of  the 
kettle  is  75  per  cent. 

Find  (a)  The  current  taken  by  the  kettle. 

(6)  The  cost  of  electrical  energy  required  for  boiling  the  water. 
N.B.  — -.  A  gallon  of  water  weighs  10  Ibs.     One  Ib.  is  equal  to 
453-6  grams. 

Temp.  F°  -  32  =  Temp.  C°- 
9  5 

Ans.  (a)  5-16  amperes. 
(6)  }d.  nearly. 


PROBLEMS  AND   EXERCISES  677 

7.  Write  down  four  equations   giving   the   value   of   the   horse- 
power expended  in  heating  a  conductor. 

(a)  In  terms  of  V  and  i. 

(b)  In  terms  of  V  and  R. 

(c)  In  terms  of  i  and  R. 

(d)  In  terms  of  Q,  V,  and  t. 
Where  i  is  the  current  in  amperes, 

V  is  the  voltage  across  the  terminals  of  the  conductor, 
R  is  the  resistance,  in  ohms,  of  the  conductor, 
Q  is  the  quantity  of  electricity  passed  in  coulombs, 
t  is  the  time  in  seconds  occupied  by  the  passage  of  the  quan- 
tity Q. 

8.  A  strong  battery-current  is  sent,  for  a  few  moments,  through 
a  bar  made  of  a  piece  of  antimony  soldered  to  a  piece  of  bismuth. 
The  battery  is  then  disconnected  from  the  wires  and  they  are 
joined  te  a  galvanometer  which  shows  a  deflexion.     Explain  this 
phenomenon. 

9.  A  long  strip  of  zinc  is  connected  to  a  galvanometer  by  iron 
wires.     One  junction  is  kept  in  ice,  the  other  is  plunged  into  water 
of  a  temperature  of  50°  C.     Calculate,  from  the  table  given  in 
Art.  474,  the  electromotive-force  which  is  producing  the  current. 

Ans.  760  microvolts. 

10.  When  heat  is  evolved  at  a  junction  of  two  metals  by  the  pas- 
sage of  a  current,  how  would  you  distinguish  between  the  heat  due 
to  resistance  and  the  heat  due  to  the  Peltier  effect  ? 

11.  Lord  Kelvin  discovered  that  when  a  current  flows  through 
iron  it  absorbs  heat  when  it  flows  from  a  hot  point  to  a  cold  point ; 
but  that  when  a  current  is  flowing  through  copper  it  absorbs  heat 
when  it  flows  from  a  cold  point  to  a  hot  point.     From  these  two 
facts,  and  from  the  general  law  that  energy  tends  to  run  down  to  a 
minimum,  deduce  which  way  a  current  will  flow  round  a  circuit 
made  of  two  half -rings  of  iron  and  copper,  one  junction  of  which  is 
heated  in  hot  water  and  the  other  cooled  in  ice. 

12.  Give  a  curve  showing  the  increase  and  decrease  of  the  thermo- 
electromotive-force  as  a  junction  of  iron  and  copper  is  raised  from 
0°  C.  to  400°  C.,  and  explain  it  by  means  of  the  thermo-electric 
diagram  of  Professor  Tait. 


678  ELECTRICITY  AND  MAGNETISM 

QUESTIONS   ON   CHAPTER  VIII 

1.  Why  in  a  continuous-current  arc  lamp  is  the  current  usually 
sent  downwards  rather  than  upwards  ? 

2.  Why  does  the  filament  of  an  incandescent  lamp  get  hotter 
than  the  metal  leading-in  wires  ? 

3.  A  current  of  9  amperes  worked  an  electric  arc  light,  and  on 
measuring  the  difference  of  potential  between  the  two  carbons  by 
an  electrometer  it  was  found  to  be  50  volts.     What  was  the  amount 
of  horse-power  absorbed  in  this  lamp ?  Ans.  0-603  H.P. 

4.  Enumerate  the  principal  parts  of  an  arc  lamp. 

5.  You  are  required  to  design  a  rheostat  for  the  use  of  a  travelling 
cinematograph  operator  who  may  wish  to  use  arcs  taking  various 
currents  between  20  and  60  amperes  in  different  towns  where  the 
supply  voltage  ranges  between  100  volts  and  240  volts. 

Find  the  maximum  and  minimum  values  of  the  resistance  of 
the  rheostat,  and  state  what  considerations  besides  these  values 
must  govern  your  selection  of  the  size  and  quantity  of  the  resist- 
ance wire  required,  and  your  design  of  the  rheostat. 

Also  calculate  the  maximum  and  minimum  costs  per  hour  run 
of  the  energy  wasted  in  the  rheostat,  rates  from  Id.  to  4d.  per 
Board  of  Trade  Unit. 

N.B.  —  Assume  the  minimum  terminal  voltage  of  the  arc  to 
be  40  volts.  Ans.  Maximum  resistance  10  ohms. 

Minimum  resistance  1  ohm. 
Maximum  cost  4s.  per  hour. 
Minimum  cost  less  than  l^d. 

QUESTIONS   ON   CHAPTER   IX 

1.  The  reluctance  (Art.  404)  of  the  core  of  a  certain  transformer 
is  0-002.     Find  the  coefficient  of  mutual  induction  between  the 
primary  and  secondary  coils  which  have  1000  and  50  turns  respec- 
tively, assuming  no  magnetic  leakage.  Ans.  0-25  henry. 

2.  A  battery  current  is  sent  through  the  primary  of  this  trans- 
former.    State  from  first   principles   the   direction    (relatively   to 
this  current)  of    the  E.M.F.s    induced  in   both   the  primary  and 
secondary,  (a)  when  the  current  is  starting,  (6)  when  it  is  ceasing. 

3.  Foucault  set  the  heavy  bronze  wheel  of  his  gyroscope  spinning 
between  the  poles  of  a  powerful  electromagnet,  and  found  that  the 
wheel  grew  hot.     What  was  the  cause  of  this?     Where  did  the 
heat  come  from? 


PROBLEMS  AND   EXERCISES  679 

4.  A  cube  is  formed  by  piling  small  square  plates  of  copper 
which  are  bound  together  with  tape.     If  this  is  hung  up  on  a 
twisted  thread  between  the  poles  of  a  powerful  magnet,  why  will 
it  twist  more  rapidly  when  the  plane  of  the  plates  is  horizontal 
than  when  it  is  vertical  ?     Also  in  the  latter  case  why  is  the  rotation 
accelerated  at  the  moments  when  the  plates  are  at  right  angles  to 
the  lines  of  magnetic  force? 

5.  You  try  to  turn  a  copper  disk  between  the  poles  of  a  magnet. 
If  you  move  it  slowly  it  goes  quite  easily,  if  you  try  to  move  it 
quickly  it  resists.     Why  is  this?     What  is  the  force  required  to 
turn  it  proportional  to  ? 

6.  The  shunt  coil  of  a  certain  dynamo  has  a  resistance  of  40 
ohms.     It  is  switched  on  to  a  battery  of  accumulators  yielding 
100  volts,   and  one   second  afterwards   the   current  has  risen  to 
0-9825   of   an  ampere.     Find   the   coefficient   of   self-induction   of 
the  shunt  coil.     Assume  log  0-607  =  1-783  and  loge  =  0-434. 

Ans.  80  henries. 

7.  If  a  battery  of  10  cells,  each  of  1-4  volt  and  2  ohms  resist- 
ance, be  applied  to  a  circuit  which  has  a  resistance  of  5  ohms  and 
inductance  0-1  henry,  find  what  modes  of  grouping  the  cells  are 
best,  (a)  to  give  the  largest  steady  current,  (6)  to  give  the  largest 
current  at  the  end  of  J^TT  second,  (c)  to  give  the  largest  amount  of 
external  work  relatively  to  the  weight  of  zinc  consumed. 

Ans.  (a)  5  in  series,  2  rows  in  parallel.     (6)  All  in  series, 
(c)  All  in  parallel. 

QUESTIONS   ON   CHAPTER  X 

1.  What  devices  are  employed  in  continuous  current  dynamos 
to  obtain  (a)  a  current  continuously  in  one  direction,  (6)  a  current 
of  uniform  strength  ? 

2.  Apply  Fleming's  Rule   (Art.  242)   to  determine  which  way 
the  electromotive-forces  will  operate  in  a  ring  armature  (gramme) 
wound  right-handedly  over  the  core  revolving  right-handedly  in 
a  horizontal  magnetic  field  having  the  N-pole  on  the  right  hand. 

Ans.  The  induced  E.M.F.s  tend  to  make  the  currents  climb, 
in  both  the  ascending  and  descending  halves,  toward 
the  highest  point  of  the  ring. 

3.  A  bipolar  dynamo's  field  magnet  gives  a  flux  of  9,000,000 
lines.     How  many   conductors   must   there   be   on   the   armature 
in  order  that  the  dynamo  may  generate  108  volts  when  driven 
at  a  speed  of  600  revolutions  per  minute?  Ans.  120. 


680  ELECTRICITY  AND  MAGNETISM 

4.  You  have  an  engine  which  will  drive  a  dynamo  at  a  fairly 
constant  speed  at  all  loads.     How  would  you  excite  the  dynamo 
if  it  were  intended  for  lighting  by  incandescent  lamps?     Make  a 
diagrammatic   sketch  of  all  necessary  connexions,   including   the 
lamp  circuit. 

5.  Take    the    equation    E  =  a  sin    (2  -n-nt).     Let    a  =  140    and 
n  =  100.     Now  take  different  values  for  t,  beginning  t  =  0-0005 
of  a  second,  then  t  =  0-001,  taking  20  different  values  until  t  = 
0-01.     Fill  in  the  values  in  the  above  equation  and  find  the  corre- 
sponding 20  values  of  E.     Then  plot  on  squared  paper,  taking  E 
as  ordinate  and  t  as  abscissae.     The  result  will  be  a  curve  like  that 
shown  in  Fig.  301. 

6.  Repeat  the  process  of  the  last  question,  taking  the  equation 
C  =  b  sin  (2  irnt  —  0),  where  6  =  20,  n  =  100,  and  0=0-5  radian. 
Plot  the  results  upon  the  same  paper  as  the  curve  in  the  last  equa- 
tion was  plotted.     One  curve  represents  the  E.M.F.  at  each  in- 
stant, the  other  the  lagging  current. 

7.  The  voltage  at  the  brushes  of  a  certain  continuous  current 
shunt  motor  is  500.     At  a  certain  load  the  mechanical  output  is 
13-5  H.P.  and  the  total  current  23  amperes.     The  resistance  of  the 
shunt  winding  under  running  conditions  is  625  ohms  and  the  arma- 
ture resistance  measured  from  brush  to  brush  is  1-3  ohms. 

(a)  Calculate  the  total  power  wasted  in  small  rotational  losses 
such  as  eddy-currents,  hysteresis,  windage  and  bearing  friction. 
(6)  Calculate  the  efficiency  of  the  motor. 

Ans.     (a)  349-8  watts. 
(6)  87-5  per  cent. 

8.  An  electric  motor  is  supplied  at  a  pressure  of  100  volts ;   the 
armature  resistance  is  0-01  ohm.     When  it  is  supplying  20  horse- 
power, what  is  its  electrical  efficiency?  Ans.  98-5  per  cent. 

9.  Show  under  what  circumstances  an  electric  motor  is  most 
efficient. 

10.  Find  the  virtual  value  —  i.e.  the  square  root  of  the  mean 
of  the  squares  —  of  the  following  series  of  numbers:  —  26,  50,  71, 
87,  97,  100,  97,  87,  71,  50,  26,  0. 

Ans.  The  sum  of  the  squares  is  60,390;  the  mean  of  the 
squares  is  5032-5;  the  square  root  of  the  mean  of  the 
squares  is  nearly  71. 

11.  An    alternating    pressure    of    100    (virtual)    volts   following 
a  sine  law  with  a  frequency  of  100  per  second  is  applied  to  the  ends 


PROBLEMS  AND   EXERCISES  681 

of  a  coil  having  a  resistance  of  8  ohms  and  a  coefficient  of  self-induc- 
tion of  0-005  henry,  find  the  current  that  will  flow  and  the  angle  of 
lag.  Ans.  Current  =  11-6  amperes;  lag  =  22  degrees. 

12.  An    alternating    current    magnet    with    properly    laminated 
core  has  a  coil  of  160  turns,  and  a  coefficient  of  self-induction  of 
0-005  of  a  henry.     What  alternating  voltage,  of  frequency  100  per 
second,  must  be  applied  to  it  in  order  to  obtain  4800  ampere-turns, 
assuming  the  resistance  to  be  negligible  ?  Ans.  94-25. 

13.  How  much  resistance  must  be  put  in  circuit  with  the  coils 
of  this  magnet  in  order  that  the  angle  of  lag  may  be  45°  ? 

Ans.  3-14. 

14.  An  alternating  current  transformer  is  designed  to  give  out 
40  amperes  at  a  pressure  of  50  volts  at  its  secondary  terminals. 
No.    of    windings    300    primary ;     12    secondary.     Resistances    12 
ohms,   primary;    0-014  ohm,   secondary.     Find  the  coefficient  of 
transformation,  and  the  volts  that  must  be  applied  at  the  primary 
of  terminals. 

Ans.  Coefficient  of  transformation  is  25;    volts  at  primary 
terminals  1283. 

15.  An  electric  welding  machine  has  its  secondary  circuit  con- 
sisting of  one  turn  of  copper  conductor,  and  its  primary  consisting 
of  80  turns  of  copper  wire.     If  a  current  of  2000  amperes  is  to  be 
induced  in  the  secondary  circuit,  how  many  amperes  must  be  im- 
parted to  the  primary?  Ans.  At  least  25  amperes. 

16.  State  the  principles  by  which  a  continuous  current  of,  say, 
25  amperes  supplied  at  1000  volts  can  be  converted  into  a  con- 
tinuous current  of  nearly  125  amperes  at  200  volts.     Why  is  it 
necessary  to  have  a  moving  part  in  continuous  current  transformers 
and  not  in  alternating  current  transformers  ? 

17.  Enumerate  three  distinct  kinds  of  alternating  current  motors, 
and  state  which  kind  is  synchronous  and  which  not. 

18.  An    alternating    current    synchronous     motor    is    supplied 
from  the  street  mains.     It  is  found  that  when  fully  loaded  it  takes 
more  current   than  when  lightly  loaded,  though  it  always  goes  at 
the  same  speed  and  the  volts  remain  constant.     Explain  how  this 
comes  about. 

19.  How  can  you  produce  a  rotatory  magnetic  field?     Describe 
some  of  its  properties. 


682  ELECTRICITY  AND   MAGNETISM 

QUESTIONS   ON   CHAPTER   XI 

1.  Certain  mains   carry  a  current   of  60  amperes  along  their 
whole  length  and  their  resistance  is  such  that  the  voltage  at  one 
end  is  100  and  at  the  other  104.     Find  (a)  the  power  supplied  to 
the  mains,  (6)  the  power  wasted  in  the  mains. 

Ans.  (a)  6J  kilowatts,  nearly.     (6)   240  watts. 

2.  Explain  why  it  is  advantageous  to  distribute  electric  energy 
at  a  high  voltage.     There  is  already  laid  a  copper  main  having  a 
resistance  of  0-5  of  an  ohm  along  which  it  is  desired  to  transit 
4  kilowatts,  and  to  deliver  it  at  the  far  end  at  a  pressure  of  100 
volts.     Which  would  be  the  more  efficient  method  of  the  two  fol- 
lowing, to  send  40  amps,  at  an  initial  pressure  of  120  volts,  or  to  send 
a  current  at  a  pressure  of  2400  volts,  using  a  transformer  with  an 
efficiency  of  85  per  cent  ? 

Ans.  The  latter  method  would  have  an  efficiency  of  84-9 
per  cent,  the  former  of  83-3  per  cent. 

3.  Explain  by  a  diagram  the  system  of  three-wire  distribution, 
and  point  out  its  advantage  over  a  two-wire  distribution. 

QUESTIONS   ON   CHAPTER  XII 

1.  What  are  the  main  points  in  the  problem  of  supplying  an  elec- 
tric current  to  a  moving  vehicle,  without  risk  of  failure  of  supply? 
How  have  these  conditions  been  met  in  practice  ? 

2.  It  is   usual   to   provide   electric   tramcars   with   two   motors 
each,  rather  than  with  one,  and  those  motors  series-wound,  rather 
than  shunt-wound.     What  are  the  reasons  for  these  preferences  ? 

3.  What  is   an   electric   controller?     What   are   the   operations 
which  it  effects  ? 

4.  Suppose  a  motor,  supplied  at  550  volts,  to  take    from    the 
lines,  during  the  period  of  acceleration,  a  current  of  220  amperes, 
how  many  electric  horse-power  are  being  supplied  at  that  time? 

Ans.  162-4. 

5.  Describe  the  arrangements  for  electric  propulsion  of  railway 
trains,  as  adopted  on  English  suburban  lines. 

QUESTIONS   ON   CHAPTER   XIII 

1.  It  is  found  that  a  single  Daniell's  cell  will  not  electrolyse 
acidulated  water,  however  big  it  may  be  made.  It  is  found,  on 
the  other  hand,  that  two  Daniell's  cells,  however  small,  will  suffice 
to  produce  continuous  electrolysis  of  acidulated  water.  How  do 
you  account  for  this? 


PROBLEMS  AND   EXERCISES  .683 

2.  From   the  table   of   electro-chemical  equivalents    (Art.   256) 
calculate  how  many  coulombs  it  will  take  to  deposit  one  grain  of 
the  following   metals:  —  Copper    (from   sulphate),   silver,   nickel, 
gold.  Ans.  Cu  196-7,  Ag  57-9,  Ni  213-1,  Au  95-1. 

3.  A  battery  of  2  Grove  cells  in  series  yields  a  current  of  5  am- 
peres for  two  hours ;  how  much  zinc  will  be  consumed,  assuming  no 
waste?  Ans.  24-39  grammes. 

4.  Calculate  the  E.M.F.  of  a  Daniell  cell  from  considerations 
of  the  heat  value  of  the  combinations  which  take  place  and  the 
quantity  of  the  elements  consumed,  taking  the  heat  value  for  zinc 
in  sulphuric  acid  as  1670  and  that  for  copper  as  909-5. 

Ans.  1-11  volts. 

5.  Describe  the  construction  and  working  of  a  modern  secondary 
battery. 

6.  Most    liquids    which    conduct    electricity    are    decomposed 
(except  the  melted  metals)  in  the  act  of  conducting.     How  do 
you  account  for  the  fact  observed  by  Faraday  that  the  amount 
of  matter  transferred  through  the  liquid  and  deposited  on  the 
electrodes  is  proportional  to  the  amount  of  electricity  transferred 
through  the  liquid  ? 

7.  Describe   the   process  for   multiplying  by   electricity   copies 
of  engravings  on  wood-blocks. 

8.  How  would  you  make  arrangements  for  silvering  spoons  of 
nickel-bronze  by  electrodeposition  ? 


QUESTIONS   ON   CHAPTER   XIV 

1.  Sketch  an  arrangement  by  which  a  single  line  of  wire  can  be 
used  by  an  operator  at  either  end  to  signal  to  the  other ;  the  condi- 
tion of  working  being  that  whenever  you  are  not  sending  a  message 
yourself  your  instrument  shall  be  in  circuit  with  the  line  wire,  and 
out  of  circuit  with  the  battery  at  your  own  end. 

2.  What  advantages  has  the  Morse  instrument  over  the  needle 
instruments  introduced  into  telegraphy  by  Cooke  and  Wheatstone  ? 

3.  Explain  the  use  and  construction  of  a  relay. 

4.  Show,  from  the  law  of  traction  (Art.  415),  that  the  change 
of  attracting  force  resulting  from  a  change  in  the  number  of  mag- 


684.  ELECTRICITY  AND  MAGNETISM 


netic  lines  that  enter  an  armature  will  be  greater  if  the  system  is 
polarized  (i.e.  magnetized  to  begin  with)  than  if  it  is  non-polarized. 
Ans.  Since  /  oc  ^2,  it  follows  that  /  +  df  will    be  propor- 
tional   to    (^  +  dft)2.        Expanding,    and    subtracting 
the  former,  and  neglecting  the    small   term    (d§)2,  we 
find  df   oc  2  ^ '  d$ ;  which  shows  that,  for  a  given  d$, 
d/ocg. 

5.  It  is  desirable  in  certain  cases  (duplex  and  quadruplex  signal- 
ling) to  arrange  telegraphic  instruments  so  that  they  will  respond 
only  to  currents  which  come  in  one  direction  through  the  line.     How 
can  this  be  done? 

6.  It  is  wished  to  make  a  sort  of  duplex  telegraph  by  using 
one  set  of  instruments  that  work  with  continuous  currents,  the 
other  set  with  rapidly  alternating  currents,  at  the  same  time  on 
the  same  line.     To  carry  out  this  idea  there  must  be  found  (a)  an 
apparatus  which  will  let  continuous  currents  flow  through  it,  but 
will  choke  off  alternate  currents  ;    (b)  an  apparatus  which  will  trans- 
mit alternate   currents,   but  cut   off   continuous  currents.     What 
apparatus  will  do  these  things? 

7.  A  battery  is  set  up  at  one  station.     A  galvanometer  needle 
at  a  station  80  miles  away  is  deflected  through  a  certain  number  of 
degrees  when  the  wire  of  its  coil  makes  12  turns  round  the  needle ; 
wire  of  the  same  quality  being  used  for  both  line  and  galvanometer. 
At  200  miles  the  same  deflexion  is  obtained  when  24  turns  are  used 
in  the  galvanometer-coil.     Show  by  calculation  (a)  that  the  inter- 
nal resistance  of  the  battery  is  equal  to  that  of  40  miles  of  the  line- 
wire  ;    (6)  that  to  produce  an  equal  deflexion  at  a  station  360  miles 
distant  the  number  of  turns  of  wire  in  the  galvanometer-coil  must 
be  40. 

8.  Suppose  an  Atlantic  cable  to  snap  off  short  during  the  pro- 
cess of  laying.     How  can  the  distance  of  the  broken  end  from  the 
shore  end  be  ascertained? 

9.  Suppose  the  copper   core   of   a   submarine   cable   to   part   at 
some  point  in  the  middle  without  any  damage  being  done  to  the 
outer  sheath  of  gutta-percha.     How  could  the  position  of  the  fault 
be  ascertained  by  tests  made  at  the  shore  end? 

10.  Explain  the  construction  and  action  of  an  electric  bell. 

11.  Describe    and    explain    how    electric    currents    are    applied 
in  the  instruments  by  which  very  short  intervals  of  time  are  meas- 
ured. 


PROBLEMS  AND   EXERCISES  685 

12.  Explain  the  use  of  Graham  Bell's  telephone  (1)  to  transmit 
vibrations  ;    (2)  to  reproduce  vibrations. 

13.  Describe  a  form  of  telephone  in  which  the  vibrations  of  sound 
are  transmitted  by  means  of  the  changes  they  produce  in  the  resist- 
ance of  a  circuit  in  which  there  is  a  constant  electromotive-force. 

14.  Two  coils,  A  and  B,  of  fine  insulated  wire,  made  exactly 
alike,  and  of  the  same  number  of  windings  in  each,  are  placed  upon 
a  common  axis,  but  at  a  distance  of  10  inches  apart.     They  are 
placed  in  circuit  with  one  another  and  with  the  secondary  wire  of  a 
small  induction-coil  of  Ruhmkorff's  pattern,  the  connexions  being 
so  arranged  that  the  currents  run  round  the  two  coils  in  opposite 
directions.     A  third  coil  of  fine  wire,  C,  has  its  two  ends  connected 
with  a  Bell's  telephone,  to  which  the  experimenter  listens  while  he 
places  this  third  coil  between  the  other  two.     He  finds  that  when 
C  is  exactly  midway  between  A  and  B  no  sound  is  audible  in  the 
telephone,  though  sounds  are  heard  if  C  is  nearer  to  either  A  or  B. 
Explain  the  cause  of  this.     He  also  finds  that  if  a  bit  of  iron  wire 
is  placed  in  A  silence  is  not  obtained  in  the  telephone  until  C  is  moved 
to  a  position  nearer  to  B  than  the  middle.     Why  is  this?     Lastly, 
he  finds  that  if  a  disk  of  brass,  copper,  or  lead  is  interposed  between 
A  and  C,  the  position  of  silence  for  C  is  now  nearer  to  A  than  the 
middle.     How  is  this  explained  ? 

QUESTIONS    ON    CHAPTER   XV 

1.  What  apparatus  would  you  use  to  produce  electric  oscilla- 
tions?    Show  how  you  would   operate  it,   and  explain  why  the 
oscillations  take  place. 

2.  Explain  how  electric  oscillations  in  a  condenser  circuit  produce 
electric  waves  in  the  surrounding  medium. 

3.  The  capacity  of  an  air-condenser    is    0-001    of    a    microfarad. 
It  is  charged  and  then  discharged  through  a  circuit  having  a  self- 
induction  of  0-004  of  a  henry  and  a  resistance  of  4  ohms.     Find  the 
frequency  of  the  vibration.  Ans.    n  =  79,600- 

4.  In  what  circumstances  do  oscillations  not  take  place  when  a 
condenser  is  discharged  ? 

5.  If  the  frequency  of  oscillation  of  a  Hertz  oscillator  is  3,000,000 
per  second,  find  the  length  of  the  waves  it  will  produce. 

Ans.   10,000  centimetres. 

6.  Explain  the  action  of  a  resonator. 

7.  What  is  the  frequency  of  the  oscillation  that  corresponds  to 
electric  waves  having  a  wave-length  of  6000  metres? 

Ans.  50,000  per  second. 


686  ELECTRICITY   AND  MAGNETISM 

8.  Give  the  reasons  which  exist  for  thinking  that  light  is  an  elec- 
tromagnetic phenomenon. 

9.  How  is  the  action  of  magnetic  forces  upon  the  direction  of 
the  vibrations  of  light  shown?  and  what  is  the  difference  between 
magnetic  and  diamagnetic  media  in  respect  of  their  magneto-optic 
properties  ? 

10.  The  resistance  of  crystalline  selenium  is  less  when  exposed 
to  light  than  in  the   dark.     Describe  the  apparatus  you  would 
employ  to  investigate  this  phenomenon.     How  would  you  proceed 
to  experiment  if  you  wished  to  ascertain  whether  the  amount  of 
electric  effect  was  proportional  to  the  amount  of  illumination? 

QUESTIONS   ON   CHAPTER   XVI 

1.  Describe  the  apparatus  necessary  for  a  transmitting  system 
in  radiotelegraphy,  and  draw  a  diagram  of  connections  of  the  system 
described. 

2.  What    is    meant    by    coupling?     Two    circuits,    inductively 
coupled,  and  tuned  to  the  same  frequency,  have  impressed  on  them 
an  oscillation  frequency  of  500,000.     It  is  found  that  this  oscillation 
is  resolved  into  two  slightly  different  frequencies  of  527,050  and 
476,730.    What  is  the  coefficient  of  coupling  of  the  two  circuits? 

Ans.    c  =  0-1. 

3.  Explain    the    difference    between    the    Quenched-Spark    and 
Oscillating-Arc  systems  of  transmission. 

4.  Describe  the  different  detectors  in  use,  and  explain  the  action 
of  each  form. 

5.  Describe  a  receiving  set  suitable  for  wireless  telephony. 

QUESTIONS   ON   CHAPTER   XVII 

1.  State  what  are  "The  Ions  of  Electrolysis,"  and  explain  their 
supposed  production. 

2.  Explain  the  phenomenon  of  ionization  of  a  gas. 

3.  Describe  an  electric  valve,  and  explain  its  action. 

4.  What  is  the  electronic  theory  of  dielectrics  ? 

5.  Describe  what  is  meant  by  a  radio-active  substance.     What 
are  the  rays  that  emanate  from  radium  ?    Distinguish  between  their 
properties. 

6.  How  is  the  ratio  between  the  electric  charge  of  an  electron 
and  its  mass  determined  ? 


INDEX 


T.Bi  —  The  Numbers  refer  to  the  Numbered  Paragraphs. 


ABSOLUTE  ELECTROMETER,  306 

Galvanometer,  226 

units,  380 

Accumulator,  Edison's,  573 
Accumulators,    572    (see    also    Con- 
denser) 

used  in  locomotion,  565 
Action  at  a  distance,  25,  66,  319 

in  medium,  6,  14,  66,  297,  319 
Aerials,  621 
Aether  (see  Ether) 
Air  condenser,  57,  314,  380 
Air-gap,  406 

Air,  resistance  of,  333,  350 
Aldini,  Giovanni,  experiments  on  Ani- 
mals, 271 
Alternating  current  magnet,  419,  533 

method    of    measuring    resistance, 
449 

motors,  547 

power,  531 
Alternating  current,  components  of, 

527 
Alternating  currents,   170,  506,  522, 

535 

Alternators,  534 
Alternators,  two  phase,  535 

three  phase,  535 

turbo-,  536 

Aluminium,  reduction  of,  579 
Amalgam,  electric,  44 

ammonium-,  sodium-,  etc.,  569 
Amalgamating  zinc  plates,  182 
Amber,  3 
Ammeter,  238 

Amoeba,  the  sensitiveness  of,  272 
Ampere,    Andre    Marie,    Theory    of 
Electrodynamics,  423 

"Ampere's  Rule,"  210,  412 

Laws  of  currents,  421,  422 

suggest  a  Telegraph,  580 

Table  for  Experiments,  422 

Theory  of  Magnetism,  430 
Ampere,  the,  169,  220,  381 
Amperemeter,  238 

-turns,  368,  405  (and  p.  669) 
Amplitude  of  E.M.F.,  522 
Angle  of  lag,  524,  525,  526 


Angles,  Ways  of  Reckoning,  147,  Ap- 
pendix A 

Solid,  151,  Appendix  A 
Animal  Electricity,  77,  273 
Anion,  255,  571,  631 
Annual  variations  of  magnet,  164 
Anode,  178,  252 
Anomalous  magnetization,  401 
Antennse,  620,  621 
Aperiodic  galvanometer,  235 
Apparent  watts,  458,  531 

resistance,  449  (c),  502  (c) 
Appropriating  brush,  50 
Arago,  Franqois  Jean 

classification  of  lightning,  355 

on  magnetic  action  of  a  voltaic  cur- 
rent, 215,  411 

on  magnetic  rotations,  500 
Arc,  the  electric,  theory  of,  486 
Arc  lamps,  487 

classification,  488 

flame,  491 

light,  486 

mechanism,  489 
Arc-lighting  machines,  514 
Armature  of  magnet,  103 
Armature    of    dynamo-electric    ma- 
chine, 506 

Armstrong,  Sir  Wm.,  his  Hydro-elec- 
tric Machine,  48 
Arresters,  lightning,  561 
Arrhenius,      Svante,      ionization     of 

liquids,  570 
Astatic  combination  (Broca's),  214 

Galvan9meter,  214,  224,  228 

magnetic  needles,  214 
Asynchronous  motors,  549 
Atmospheric  Electricity,  73,  353 
Atoms,  charge  of,  570  (footnote) 

electronic  constitution  of,  640 
Attracted-disk  Electrometers,  306 
Attraction  and  repulsion  of  electrified 
bodies,  3,  5,  22,  24,  75,  279 

and  repulsion  of  currents,  420 

and  repulsion  of  magnets,  85,  90, 
362 

due  to  influence,  24 
Aurora,  the,  165,  166,  168,  361 


687 


688 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Automobiles,  electric,  565 

Ayrton  and  Mather  galvanometer,  229 

Ayrton  (W.  E.)  and  Perry  (John) 

amperemeter,  238 

on  contact  electricity,  81 

secohmmeter,  502  (c) 

value  of  "v,"  386 
Azimuth  Compass,  152,  157 

B.  A.  UNIT,  385 

Back  E.M.F.,  519 

Back  Stroke,  29 

Bain,    Alex.,    his    Chemical   Writing 

Telegraph,  262 
Balance  Methods,  141,  443,  445  et  seq. 

Wheatstone's,  445 
Ballistic  Galvanometer,  234,  451 
Bancalari  on  flames,  402 
Barrett,  Sir  William,  on  magnetic  con- 
traction, 125 
Batteries,  voltaic,  176,  187,  202 

secondary,  572 
Battery  of  Leyden  jars,  63 
Bauer,  Louis  Agricola,  magnetic  sur- 
vey, 161 

Beccaria,  Father  G.,  on  electric  distil- 
lation, 267 

on  atmospheric  electricity,  358 
Becquerel,  \Antoine  Cesar,  on    atmos- 
pheric electricity,  359 
Becquerel,  Antoine  Cesar,  on  diamag- 

netism,  398 
Becquerel,  Edmond,  on  photo-voltaic 

currents,  618 
Becquerel,    Henri,    on   magneto-optic 

rotation,  613 

discovers  radio-activity,  638 
Bell,    Alexander    Graham,    his    Tele- 
phone, 593 
Uses  induction  balance  to  detect 

bullet,  597 

The  Photophone,  617 
Bells,  electric,  591 
Bennet,  Abraham,  his  doubler,  49 

Electroscope,  17,  28 
Best  grouping  of  cells,  207,  439 
Bichromate  Cell,  189,  204 
Bidwell,   Shelford,   on  magnetic  con- 
traction, 125 
on  susceptibility,  392 
on  lifting  power,  415 
Effect  of  light  on  magnets,  611 
Bifilar  Suspension,  132,  222,  307 
Biot,  Jean  Baptiste,  experiment  with 

hemispheres,  33 

Law  of  magnetic  distribution,  159 
on  atmospheric  electricity,  359 
Birkeland,  Kristian,  nitrates  from  air, 
336,  469 


Bismuth,  diamagnetic  properties  of, 

98,  399 

change  of  resistance  in  magnetic 
field,  429 

Blasting  by  electricity,  336,  467 

Blondel,     Andre,     his     oscillograph, 
236 

Blood,  conducting  power  of,  272 

Board  of  Trade  Standards,  Appendix 
B 

Board  of  Trade  Unit,  558 

Bolometer,  436 

Bolton,  von,  tantalum  filament,  481 

Boltzmann,     Ludwig,     on     Dielectric 
capacity,  317,  609 

Boracite,  75 

Bosanquet,  R.  H.  M.,  magnetic  cir- 
cuit, 403. 

"Bound"  electricity,  27,  80 

Boyle,  Hon.  Robert,  3  (footnote) 

Boys,  Charles  Vernon,  radio-microm- 
eter, 478 

Brake,  eddy-current,  460,  500 

Brake-wheel  arc  lamps,  489 

Branched  circuit,  441 

Branly,  Edouard,  filings  coherer,  606 

Brass,  deposition  of,  569 

Breaking  a  magnet,  93 

Breath-figures,  348 

Bridge,  Wheatstone's,  445 

British  Association  Unit,  385 

Broadside-on  Method,  140 

Broca,.  Andre,  his  astatic  pair,  214 

Brown,  Sidney  George,  relay  of,  598 

Brugmans  discovers  magnetic  repul- 
sion of  bismuth,  398 

Brush,  Charles  F.,  his  dynamo,  514 

Brush  discharge,  340,  348 

Brushes,  508 

Bunsen's  cell,  191,  204 

CABLE,  Atlantic,  322,  323,  347,  587, 
588 

submarine,  587 

as  condenser,  322,  347. 
Cadmium  in  standard  cell,  201 
Cailletet  on  resistance  of  air,  333 
Calc-spar,  76 

Calibration  of  Galvanometer,  224 
Callan,  induction  coil,  246 

Battery,  191  (footnote) 
Callaud's  cell,  198 
Calender's  pyrometer,  436 
Calomel  cell,  200 
Calories  and  joules,  459,  462 
Canal  rays,  344 
Candles,  electric,  492 
Canton,  John,  discovers  electrostatic 
induction,  22 


INDEX 


689 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Capacity,  definition  of,  289 

in  alternate  circuit,  528 

measurement  of,  451 

of  cable,  322  et  seq. 

of  condenser,  59,  314,  325,  528 

of  conductor,  41,  57,  290,  325 

of  Leyden  jar,  59,  314 

of  liquid  condenser,  572 

specific  inductive,  25,  57,  315,  317 

unit  of  (electrostatic),  290 

unit  of  (practical),  323 
Capillary  Electrometer,  269,  312 
Carbon   plates   and  rods,    191    (foot- 
note) 

filaments,  482 

glow-lamps,  482 
Carbons  for  arc  lamps,  487 
Cardew,  Philip,  his  voltmeter,  465 
Carnivorous  Plants,  sentitive  to  elec- 
tricity, 272 
Carriers,  49 
Cars,  electric,  563 
Castelli,  Paolo,   telephonic  reception 

of  wireless  signals,  620 
Cautery  by  electricity,  466 
Cavallo,  Tiberius,  his  attempt  to  tele- 
graph, 580 

on  atmospheric  electricity,  358 
Cavendish,  Hon.  H.,  on  Specific  In- 
ductive capacity,  315,  316 

on  nitric  acid  produced  by  sparks, 
336 

experiment     with     hollow     hemi- 
spheres, 33 

Ceca,    Father,    on    atmospheric  elec- 
tricity, 358 
Cell,  Bichromate,  189 

Bunsen's,  191 

Clark  (Standard),  200 

Daniell's,  196 

Grove's,  190 

Lalande's,  194 

Leclanche's,  192 

voltaic,  174 

Weston  (Standard),  201 
Cells,  classification  of,  185 

"dry,"  193 

grouping  of,  207,  439 

list  of,  204 

photo-chemical,  618 

standard,  200,  201 
Centi-ampere  balance,  427 
Central  stations,  554 
Change  of  configuration,  law  of,  217, 

409 

Characteristic  curves,  512 
Charge,  distribution  of,  40 

electric,  9 

resides  on  surface,  32 

2Y 


Charge,  residual  of  Leyden  jar,  62,  319 

of  accumulator,  572 
Chart,  magnetic,  161  (frontispiece) 
Chemical  action,  E.M.F.  of,  567 
Chemical  actions  in  the  battery,  180 

laws  of,  186,  256,  567 

of  spark  discharge,  336 

outside  the  battery,  250,  566 
Chemical  test  for  weak  currents,  262, 
336 

depolarization,  185 
Chimes,  electric,  46 
Choking-coils,  530 
Choking-effect,  474,  503,  526,  530 
Chromic  solution,  191 
Chronograph,  electric,  592 
Circuit,  169,  174,  406,  438 

inductive,  525 

Magnetic,  403 

points  of,  where  energy  gained  and 

lost,  264,  455 

Circuital  magnetism,  120,  374 
Circuits,  branched,  261,  441 
Circular  current,  372 
Clamond's  thermopiles,  477 
Clark,  Latimer,  his  standard  cell,  200 
Classification  of  cells,  185 
Clausius,  Rudolf,  theory  of  Electroly- 
sis, 570 

Cleavage,  electrification  by,  69 
Clock  diagram,  522,  525 
Clocks,  electric,  592 
Closed  circuit,  cell  for,  184,  196 
Closed-circuit  method  of  Telegraphy, 

583 

Closed-coil  armature,  508 
Cobalt,  magnetism  of,  97 
Coefficient  of  Magnetic  induction  (see 
Permeability) 

of    Magnetization    (see    Suscepti- 
bility) 

of  mutual-inductance  (or  potential) 
378,  497 

of  self-inductance,  501 
Coercive  force,  8,  394 
Coherer,  filings,  606 
Colour  of  spark,  339 
Columbus,     Cristofero,    on    magnetic 

variation,  157 

Combs  on  influence  machine  43,  50 
Combustion  a  source  of  electrifica- 
tion, 71 

heat  of,  567 

Commutator,  506,  508,  516 
Compass   (magnetic),  Lord  Kelvin's, 
153 

errors,  correction  of,  155 

floating,  154 

Kelvin-Chetwynd,  154 


690 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Compass  (magnetic),  Mariner's,  89, 
152 

error  due  to  iron  ship,  152 
Compound  circuit,  207,  261,  441 

dynamo,  511,  513 

magnets,  104 

Compression,  electrification  due  to,  74 
Condensation,  57 
Condenser,  57,  314,  322,  333 

capacity  of,  how  measured,  451 
Condenser,  discharge  of,  350,  600 

in  alternating  circuit,  526,  528 

liquid,  572 

method  of  measuring  a  resistance, 
443,  449 

Moscicki's,  63 

standard,  333 

use  of,  246,  322 
Condensing  electroscope,  80 
Conductance,  434,  436 

unit  of,  381 
Conduction,  8,  30,  179,  434,  436,  532 

by  liquids,  250,  436 

in  solids,  635 

of  gases,  179,  345,  633 
Conductivity,  179,  345,  434,  436 
Conductor  cutting  lines,  243,  366,  380 

384 
Conductors  and  Non-conductors,  9, 

27,  30,  434  et  seq. 
Conductors  electrified  by  rubbing,  13 

opaque,  609 

Consequent  Poles,  119,  122,  412 
Constant-current  dynamos,  514 

voltage  dynamos,  513 
Contact  Electricity,  80,  171 

Series  of  metals,  81 

of  surfaces,  13 
Continuous  current  converters,  545 

current  generators,  508 

current  transformers,  545 

currents,  169 

electrophorus,  26,  49 
Contraction  due  to  magnetism,  125 
Control  of  galvanometer,  222 
Convective  discharge,  332 
Conversion,  the  problem  of,  544 
Converters,  544,  545,  546 

continuous-current,  545 

rotatory,  546 

synchronous,  546 
Convection  of  electricity,  49,  332, 429 

currents,  429 

induction  machines  (see  Influence 
machines) 

streams  at  points,  38,  47,  292,  353 
Cooking  by  electricity,  470 
Cooling  and  heating  of  junction  by 
current,  471 


"Corkscrew  Rule,"  211 
Corona  discharge,  341 
Cost   of    power   derived    from    elec- 
tricity, 558 
Coulomb,   Auguste,   experiment  with 

hollow  hemispheres,  33 
Torsion  Balance,  18,  134 
Law  of  Inverse  Squares,  19,  131, 

134,  278,  288 

on  distribution  of  charge,  38,  291 
Coulomb,  the,  169,  391 

how  many  electrostatic  units,  279 

(footnote) 

Couple,  magnetic,  138 
Coupling,  623 

of  alternators,  537 
of  circuits  by  a  transformer,  543 
Creeping,  stopped  by  paraffin,  191 

magnetic,  395 
Crookes,  Sir  William,  on  shadows  in 

electric  discharge,  343 
on   repulsion   from   negative   elec- 
trode, 351 

Crossed  fields,  method  of,  639 
Crown  of  cups,  173 
Cruickshank's  Trough  Battery,  188 
Crystallization,  70 
Crystals,  electricity  of,  75,  76 
dielectric  properties  of,  317 
magnetism  of,  401 

Gumming,     James,     invents     galva- 
nometer, 213 

thermo-electric  inversion,  475 
Cuneus'    discovery    of    Ley  den    jar, 

61 

Curbing  telegraphic  signals,  322 
Curie,  Madame  Marie,  discovery  of 

radium,  638 
Current,  components  of  alternating, 

527 

effects  due  to,  175 
Electricity,  169 
strength  of,  179,  205 

„  unit  of,  169,  220 

Current,  is  the  magnetic  whirl,  215 
balance,  427,  and  Appendix  B 
sheets,  442 
Currents,  very  large,  measurement  of, 

444 
Curvature  affects  surface-density,  38, 

292 

Curve-tracer,  395 
Curves,     magnetic      (see     Magnetic 

Figures) 
Curves  of  magnetization,  391 

characteristic,  of  dynamos,  512 
Cycles  of  magnetization,  395 
Cycles  of  alternate  currents,  522 
Cylinder  electrical  machine,  43 


INDEX 


691 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


DAILY  variations  of  compass,  163 
Dalibard's  lightning  rod,  353 
Damping,  600 

galvanometers,  235 
Daniell,  John  F.,  his  cell,  196,  204 
D'Arsonval,  galvanometers,  229 
Davy's  (Marie)  Cell,  204 
Davy,   Sir  Humphry,    magnetization 
by  current,  411 

discovers  electric  light,  486 

electrolyses  caustic  alkalies,  569  (c) 
De  Haldat,  magnetic  writing,  124 
De  la  Rive's  Floating  Coil,  218 
De  la  Rue,  Chloride  of  silver  battery, 
197,  333 

on  electrotyping,  576 

on  length  of  spark,  333 
Dead-beat  galvanometers,  235 
Declination,  Magnetic,  157 

variations  of,  157,  162 
Decomposition  of  water,  251 

of  alkalies,  569  (c) 
De-electrification  by  flame,  334 
Deflexion  of  galvanometer,  223 
Deflexions,  method  of,  133,  138 
Dellmann's  electrometer,  305 
Demagnetize,  how  to,  395 
Density  (surface)  of  charge,  38,  291 

magnetic,  136,  363 
Depolarization,  mechanical,  185,  188 

chemical,  185,  189 

electro-chemical,  185,  195 
Deposition  of  metals,  575 
Detectors  of  electric  waves,  606,  626 
Deviation  of  compass,  152 
Dewar,  James,  on  currents  generated 
by  light  in  the  eye,  273 

his  capillary  electrometer,  269 

magnetic    properties    of    iron    at 
-  180°,  114 

oxygen  magnetic,  398 
Dewar  and  Fleming,  resistance  at  low 

temperature,  436 
Diagram,  thermo-electric,  476 
Dial  bridge,  447 
Diamagnetic  data,  399 

polarity,  398 
Diamagnetism,  98,  398 

of  flames,  402 

of  gases,  398,  402 
Diaphragm  currents,  268 
Dielectric,  action  across,  56 

capacity,  315  to  319 

capacity,    effect    on    intensity    of 
field,  279,  318 

coefficient,  301,  609 

rigidity,  335 

strength,  335 
Dielectrics,  11,  25,  57,  315,  636 


Difference  of  potential,  283 

magnetic  potential,  362 
Differential  galvanometer,  233,  443 
Dimensions  of  units,  383 
Dip,  or  Inclination,  158 

variation  of,  162 
Diplex  signalling,  586 
Dipping  needle,  158 
"Direct" and  "inverse"  current,  240 
Direction  of  induced    E.M.F.,    242, 

499 
Discharge  affected  by  magnet,  346 

brush,  340,  348 

corona,  341 

by  evaporation,  267 

by  flame,  9,  334 

by  points,  47,  340,  353 

by  water  dropping,  359 

conductive,  330 

convective,  47,  332 

disruptive,  331 

effects  of,  47,  335,  336,  337 

glow,  340,  353  (footnote) 

ionization  by,  346 

limit  of,  291 

oscillatory,  600 

sensitive  state  of,  346 

striated,  342 

through  gas  at  low  voltage,  346 

velocity  of,  347 

Discharger,  Discharging-tongs,  60 
Displacement,  electric,  58 

currents,  601 

Disruption,  electrification  by,  69 
Dissectable  Ley  den  jar,  65 
Dissipation  of  Charge,  350 
Dissociated  gases  conduct,  346 
Distillation,  electric,  267 
Distortion  of  dynamo-field,  508 
Distribution  of  Electricity,  31  to  38, 
291,  292 

of  Magnetism,  119,  136 
Distribution  by  transformers,  538 
Distribution  of  energy,  554 
Distributors,  557 
Divided  circuits,  441 
Divided  Touch,  106 
Dolbear,  A.  E.,  his  telephone,  319,  593 
Doubler,  the,  26,  49 
Double  refraction  by  electric  stress, 

611,  612 

Double  Touch,  107 
Drop  of  voltage  in  mains,  444,  447, 

551 

Dry  cells,  193 
Dry-Pile,  203,  311 
Du  Bois,  limit  of  magnetization,  390 

measurement  of  permeability,  393 
Du  Fay's  experiments,  6,  30 


692 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Duddell,  William,  oscillograph,  236 

his  singing  arc,  495 

his  thermo-galvanometer,  478 
Duplex  Telegraphy,  322,  586 
Duration  of  Spark,  347 
Dust,  allaying,  54 
Duter  on  Electric  Expansion,  320 
Dynamic    Electricity     (see    Current 

Electricity) 

Dynamo  calculations,  510 
Dynamometer,  425 
Dynamos,  507 

as  motors,  516,  508 
Dyne,  the  (unit  of  force),  299 

EARTH,  the,  a  magnet,  94 

currents,  322 

electrostatic  capacity  of,  323 

magnetic  force  in  absolute  units, 
388 

used  as  return  wire,  580 
Earth's    magnetism    (see    Terrestrial 

Magnetism) 
Earth,  potential,  287 
Eddy-current  brake,  460,  500 
Eddy-currents,  500,  533,  549 
Edison,  Thomas  Aha,  his  accumula- 
tor, 573 

carbon  telephone,  594 

electric  lamp,  481 

meter  for  currents,  260,  460 

quadruplex  telegraphy,  586 
Eel,  electric  (Gymnotus),  77 
Effect  of  various  loads  on  power 

station,  560 
Efficiency,  456 

of  transmission,  551 

of  dynamos,  510 

of  motors,  519 

of  transformers,  541 
Electric  Air-Thermometer,  337 

automobiles,  565 

Cage,  37 

Candle,  492 

Clocks,  592 

Displacement,  58 

Distillation,  267 

Egg,  the,  342 

Expansion,  320 

Field,  14,  17,  20,  22,  24,  279,  297, 
611,  612 

Force,  177  (footnote),  284 

(Frictional)  machines,  43 

furnace,  469 

Fuse,  337,  464,  467 

Images,  293 

Kite,  353 

Light,  486 

Lines  of  Force,  14, 17, 20, 22, 24, 319 


Electric  locomotion,  562 

Mill  or  Fly,  47 

Oscillations,  600 

Osmose,  266 

Pistol,  336 

railways,  564 

Shadows,  343 

Shock,  270 

Stress,    14,    17,    20,    22,    24,    65, 
297 

tramways,  563 

valves,  432,  634 

Waves,  600,  601 

Wind,  47,  348 
Electrics,  3 
Electricity,  theories  of,  8,  351 

word  first  used,  3  (footnote) 
Electrification,  positive  and  negative, 
8,  351 

sources  of,  13,  67  et  seq. 
Electrocapillary  phenomena,  269 
Electrochemical  Depolarization,  185, 
195 

energy,  567 

equivalents,  256,  568 

power  of  metals,  568 
Electrochemistry,  566 

deposition,  575 
Electrodes,  252 

unpolarizable,  273 
Electrodynamics,  420 
Electrodynamometer,  425 
Electrolysis,  252,  566 

in  discharge,  346 

laws  of,  256,  569 

of  copper  sulphate,  254 

of  water,  253,  566 
Electrolysis,  the  ions  of,  631 

theory  of,  570 
Electrolytes,  252,  566 

resistance  measurement  of,  450 
Electrolytic  condenser,  572 

convection,  570 

furnaces,  579 

Electromagnet,    alternating    current, 
533 

half-ring  type,  413 

plunger,  416 
Electromagnets,  110,  411,  413,  416 

and  permanent  magnets,   contrast 
between,  407 

laws  of,  410 

calculations  for,  403,  404  (and  see 

p.  669) 
Electromagnetic  engines  (see  Motors) 

systems,  law  of,  217,  409 

system  of  units,  379 

theory  of  Light,  609 

waves,  600 


INDEX 


693 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Electromagnetics,  362 
Electromagnetism,  362 
Electrometallurgy,  575 
Electrometer,  absolute,  306 

attracted-disk,  306 

capillary,  269,  312 

Dellmanris,  305 

Peltier's,  305,  359 

portable,  306 

quadrant  (Lord  Kelvin's),  307 

repulsion,  305 

torsion,  18 

Wilson's,  310 
Electromotive-force,  177,  566 

induced,  239 

measurement  of,  448 

unit  of,  381 

Electromotive  intensity,  284,  301 
Electromotors,  516,  547 
Electron,  1,  8,  22,  630  et  seq. 

numerical  estimates  of,  630 

emission  by  hot  bodies,  632 
Electrons  in  dielectrics,  636 

in  motion,  magnetic  forces  of,  637 

and  radio-activity,  638 
Electronic  constitution  of  atoms,  64U 
Electro-Optics,  611 
Electrqphorus,  26 

continuous,  26,  49 
Electroplating,  577 
Electroplating,  dynamos  for,  507 
Electroscopes,  15 

Bennet's  gold-leaf,  17,  28 

Bohnenberger's,  17,  311 

Fechner's.  311 

Gilbert's  straw-needle,  16 

Hankel' s,  311 

Pith-ball,  4,  5 

Yalta's  condensing,  80 
Electroscopic   powders,   31,  47,   319, 

348 
Electrostatic  Optical  Stress,  612 

voltmeter,  309 
Electrostatics,  9,  276 
Electrotyping,  576 
Element  of  Current,  371 
End-on  method,  140 
Energy,  1,  66 

electrochemical,  567 

long-distance  transmission  of,  552 

of  magnetic  field,  215 

of  charge  of  Leyden  jar,  326 

of  electric  current,  454 

paths,  610 

points  in  circuit  where  it  is  lost  or 
gained,  264,  455 

relations,  539 

supply  and  measurement  of,  454 
Equator,  Magnetic,  88 


Equipotential  surfaces,  285 

magnetic,  362  (/) 
Equivalents,  electrochemical,  256 
Erg,  the  (unit  of  work) ,  299 
Ether,  1,  8,  66,  609 
Evaporation  produces  electrification, 

72,  354 

discharge  by,  267 
Everett,    James   D.,    on    atmospheric 

electricity,  259 

Evershed,  Sydney,  resistance  of  insula- 
tors, 437 

Ewing,  James  A.,  on  limit  of  mag- 
netization, 390 
curves  of  magnetization,  391 
theory  of  magnetism,  129 
Exchanges,  telephone,  596 
Excitation  of  Field-magnets,  511 

and  speed  of  motors,  521 
Expansion,  electric,  320,  612 
Extra-current,  503 

Eyde,  Samuel,  production  of  nitrates 
from  the  air,  336 

FAILURE  and  exhaustion  of  batteries, 

180 
Fall  of  potential  along  a  wire,  308, 

444 

Farad,  the  (unit  of  capacity),  323,  381 
Faraday,   Michael,   molecular  theory 

of  electricity,  8 
chemical  theory  of  cell,  186 
dark  discharge,  340 
diamagnetism,  398,  401,  402 
discovered  inductive  capacity,  25, 

316 
discovery    of    magneto-induction, 

239 

Disk  machine,  244 
electro-magnetic  rotation,  428 
experiment  on  dielectric  polariza- 
tion, 319" 

gauze-bag  experiment,  34 
hollow-cubo  experiment,  34 
ice-pail  experiment,  37 
laws  of  electrolysis,  256,  258 
length  of  spark,  333 
Magnetic  lines-of-force,  121 
magnetism  in  crystals,  401 
on  Arago's  rotations,  500 
on  dissipation  of  charge,  334 
on  electrodynamics,  423 
on   identity   of    different    kinds  of 

electricity,  261,  262,  336 
predicted  retardation  in  cables,  321 
Ring,  245 
rotation  of  plane  of  polarized  light, 

613 
voltameter,  258 


694 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Faure,  Camille,  his  Secondary  Bat- 
tery, 572 

Favre's  experiments  on  heat  of  cur- 
rents, 463 

Fechner's  electroscope,  311 
Feddersen,  W.,  on  electric  oscillations, 

600 

Feeders,  555 

Ferromagnetic  substances,  396 
Field,  electric,  14,  17,  20,  22,  24,  279, 

297,  612 

magnetic,  118,  215,  362,  507,  613 
Field-magnet,  462,  507 
Field-magnets,  excitation  of,  511 
Field-plate,  50 

Figures,     magnetic     (see     Magnetic 
-    figures') 

electric,  31,  319,  348 
Filament  of  incandescent  lamps,  481 
Filings  for  mapping  fields,  123 

coherer,  606 

Fire  of  St.  Elmo,  353  (footnote) 
Flame,  currents  of,  334 
arc  lamps,  491 
diamagnetism  of,  402 
discharge  by,  9,  334 
produces  electrification,  71  . 
"Flashing"  filaments,  482 
Fleming  and  Dewar,  resistance  at  low 

temperature,  436 

Fleming,  John  Ambrose,  his  Cell,  202 

rule  as  to  direction  of  E.M.F.,  242 

Flux,  magnetic,   143,  363,  364,  390, 

405,  density,  390  (footnote) 
Fog,  dispersal  of,  55 
Fontana  on  electric  expansion,  320 
Force,    electric,    177    (footnote),   284, 

294,  295 

electromotive     (see    Electromotive- 
force) 

magnetic,  95,  177  (footnote),  362 
near  a  straight  conductor,  220,  370 
on  conductor  in  field,  367,  368 
Form,  effect  of,  on  retentivity,  101 

on  lifting  power,  117 
"Forming"  accumulator  plates,  572 
Foster,  George  Carey 

method  of  testing,  447 
Foucault,  Leon,  his  Regulator  Lamp, 

487 

Interrupter,  247 

Foucault-currents  (see  Eddy-currents) 
Franklin,   Benjamin,   discovered   ac- 
tion of  points,  mentioned  in,  38 
(c),  47,  353 
cascade    arrangement    of    Leyden 

jars,  329 

Electric  chimes,  46 
Electric  kite,  353 


Franklin,  Benjamin, Electric  portraits, 
337 

his  charged  pane  of  glass,  56 

invents  lightning  conductors,  353, 
356 

kills  turkey  by  electric  shock,  270 

One-fluid  theory  of  electricity,  8 

on  seat  of  charge,  65 
Frankfort,  transmission  of  power  to, 

551,  548  (footnote) 

"Free"  electricity,  27,  80  (footnote) 
Frequency,  522,  532 

measurement,  604 

of  oscillations,  600,  605 
Friction   produces   electrification,   3, 

13 

Frictional  machines,  42 
Frog's  legs,  contractions  of,  171,  271 
Frolich,  Otto,  on  electromagnet,  410 
FromenCs  motor,  516 
Fuel,  zinc  as,  174 
Furnace,  electric,  469 

electrolytic,  579 
Fuses,  337,  464,  467 
Fusing  of  wires,  464 

"G"  of  galvanometer,  226 
Galvani,    Aloysius,    observed    move- 
ments of  frog's  leg,  171 

on  preparation  of  frog's  limbs,  271 

on  Animal  Electricity,  273 
Galvanic  Batteries  (see  Voltaic  Bat- 
teries) 

Electricity  (see  Current  Electricity) 

Taste,  270 

Galvanism  (see  Current  Electricity) 
Galvanometer,  221 

absolute,  226 

astatic,  214,  224,  228 

ballistic,  234,  451 

Broca's,  231 

constant  of,  226 

damping  of,  235 

D'Arsonval's,  229 

dead  beat,  235 

differential,  233,  443 

Du  Bois  Reymond's,  273 

reflecting  (Lord  Kelvin's) ,  or  mirror, 
228 

shunts,  230 

sine,  227 

string,  232 

tangent,  225 

Von  Helmholtz's,  225 
Galvanoplastic  (see  Electrotyping) 
Galvanoscope,  212 
Gas  Battery,  574 
Gases,  dissociated,  conduct,  346 

resistance  of,  179,  334,  346 


INDEX 


695 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Gassiot,  J.  P.,  on  striae,  351 
Gauss,  C.  F.,  on  magnetic  shell,  375 
Gay-Lussac,  on  atmospheric  electric- 
ity, 359 

Geissler's  tubes,  342 
Generators   of   alternating   currents, 

534 

continuous  currents,  508 
Gibson  and  Barclay  on  dielectric  ca- 
pacity of  paraffin,  317. 
Gilbert,  Dr.   William,  discovers  elec- 
trics, 3 

discovered  magnetic  reaction,  95 
discovers  that  the  earth  is  a  mag- 
net, 94,  156 

heat  destroys  magnetism,  112 
his    balanced-needle    electroscope, 

16 

his  terrella,  94 
observation  of  moisture,  11 
observations  on  magnets,  88 
on  de-electrifying  power  of  flame, 

334 

on  magnetic  figures,  121 
on  magnetic  substances,  96 
on  magnetic  permeability,  100 
on  methods  of  magnetization,  108, 

109 

writings  of,  88 

Glass,  a  conductor  when  hot,  31 
Globular  lightning,  355 
Glow  Discharge,  340,  353  (footnote) 

lamps,  481,  482,  483 
Gold-leaf   Electroscope    (see  Electro- 
scope) 

Goldschmidt,  high-frequency  alterna- 
tor, 622 

Gordon,  J.   E.  H.,  on  dielectric  ca- 
pacity, 317 

Gramme,  Zenobe  Theophile,  his  ring- 
armature,  508 
Gravity  Battery,  198 
Gray,    Andrew,    Absolute    Measure- 
ments in  E.  and  M:,  138  (foot- 
note),  306    (footnote),   427    (foot- 
note) 
Gray,  Stephen,  discovers  conduction, 

30 

on  lightning,  353 
Grid  of  accumulator,  572. 
Grotthuss'  theory,  180,  570 
Grouping  of  arc  lamps,  487 
cells,  207,  439 
glow-lamps,  482 

Grow,  Sir  William  R.,  his  Gas  Bat- 
tery, 574 
Grove's  Cell,  190 

magnetic  experiment,  125 

on  electric  property  of  flame,  334 


Guard-ring,  Guard-plate,  291,  306 
Guericke,  Otto  von,  discovered  electric 

repulsion,  5 

invents  electric  machine,  42 
observes  electric  sparks,  12 
Gunpowder  fired  by  electricity,  336, 

337,  467 
Guthrie,  Frederick,  effect  of  heat  on 

discharge,  334 

heating  of  kathode  in  water,  468 
Gymnotus  (electric  eel),  77,  262 

HADFIELD,  SIR  ROBERT  A.,  391 
Half  deflexion  method,  449 
Hall,  Edward  H.,  his  effect,  429 
Hamilton,  James,  law  of  lift  of  mag- 
net, 117 
Hankel,  Wilhelm  G.,  his  electroscope, 

311 

Hardening  of  steel,  111 
Harris,  Sir  W.  Snow,  his  unit  Ley- 
den  jar,  304 

attracted-disk  electrometer,  306 
on  length  of  spark,  333 
Hauksbee,  Francis,  on  thunderstorms, 

353 
Haiiy,  The  Abbe,  his  astatic  method, 

214 

Heat  and  resistance,  459,  461 
of  combination,  567 
effect  of,  on  magnets,  112,  114 

cells,  199 

„  Geissler  tube,  342 

,,  resistance,  436 

emission,  417,  464 
Heat,  unequal  action  of,  on  +  and  — 

charges,  327,  334 
Heating  of  coils,  417,  464 
Heating  effects  of  currents,  190,  459, 

461 

due  to  magnetization,  125,  395 
effect  of  sparks,  337 

,,        dielectric  stress,  319 
local,  at  electrodes,  569 
Heaviside,     Oliver,     reluctance,     403 

(footnote) 

on  energy  paths,  610 
on  quadruplex  telegraphy,  580 
Helmholtz,    Hermann   L.   F.   von,    on 

effect  of  current  on  sight,  270 
Electrolytic  convection,  570 
Equations  of  self-induction,  504 
Galvanometer,  225 
Hemihedry  in  crystals,  76 
Henry,       Joseph,       invented        the 

"sounder,"  580 
on    induced     currents     of     higher 

orders,  498 
Henry,  the,  381,  497,  501 


696 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Hertz,   Heinrich,   on  effect  of  ultra- 
violet waves,  333,  619 
kathode  rays,  344 
researches  on  electric  waves,  605 
Heusler's  alloys,  396- 
Heydweiller,  on  length  of  spark,  333 
High  frequency,  532,  600,  605 

„  „         apparatus,  603 

High  voltage  jars,  64 
Hittorf, .  Wilhelm,    on  electroplating, 

577 

on  discharge,  346 

Holtz,  W.,  his  electric  machine,  53 
on  tubes  having  unilateral  resist- 
ance, 351 

Homopolar  Dynamo,  515 
Hopkinson,    John,   on   dielectric   ca- 
pacity of  glass,  317 
on  residual  charge  and  its  return, 

319 

on  magnetization,  391 
his  characteristic  curves,  512 
Horizontal  component  of  magnetism, 

138,  159,  388 
Horn  gap  arrester,  561 
Horse  power  and  watts,  454 
Hot  glass,  a  conductor,  31 
Hughes.  David  Edward,  the  Printing 

Telegraph,  580 
the  Microphone,  595 
induction  balance,  597 
Humboldt,  Alexander  von,  on  electric 

eels,  77 

discovers  galvanic  smell,  270 
produced   electric    contractions   in 

fishes,  271 
Hunter,  Dr.  John,  on  effect  of  current 

on  sight,  270 

Hydroelectric  machine,  48 
Hysteresis,  394,  395 

IDIOSTATIC    method    of    using    volt- 
meter, 309 
Images,  electric,  293 
Impedance,  525,  526 
(Impedance)  coils,  530 
Impulsive  rush,  357 
Incandescent  lamps,  481,  482,  483 
Inclination  (or  Dip),  158 

variation  of,  162 
Index  Notation,  382 
Induced  charges  of  electricity,  22 

currents,  239 
Inductance,  501 
Induction  (electrostatic)  of  charges 

(see  Influence) 
Induction  (magnetic)  lines  of,  99 

(magnetic)  of  magnetism,  99 

(magneto-electric)  of  currents,  239 


Induction  (vclta-electric)^  of  currents  by 
currents  (see  Self-induction,  Mu- 
tual induction) 

the,  meaning  the  internal  magnet- 
ization, 390  (footnote) 
Induction-coil  or  Inductorium,  246 
Induction-convection  machines,  49 
Inductive-capacity,   specific,  25,   57, 

315,  319 

Inductive  circuits,  525 
Inductivity,  315,  317,  318 
Inertia,  electromagnetic,  501 
Influence,  22 
Influence-machine,  49—54 
Insulators,  11,  30,  437 
Intensity  of  current,  205  (footnote) 

of  earth's  magnetic  force,  159,  388 

of  magnetic  field,  365 

of  magnetization,  392 
Internal  resistance,  179,  438,  449 

of  armatures,  507 
International  ohm,  385 
Interrupters,  247 

"Inverse"  and  "direct"  currents,  240 
Inverse  Squares,  Law  of,  19,  131,  151, 

278,  288 

Inversion,  Thermo-electric,  475 
lonization,  632 

by  discharge,  346 
Ions,  255 

Ironclad  magnet,  413 
Iron,  properties  of,  389 
Iron  rods  red-hot  in  water,  468 
Isoclinic  lines,  161 
Isogonic  lines,  161 
Isolated,  289 

JABLOCHKOFF,  PAUL,   his   battery, 

202 

electric  candle,  492 
Jacobi,    Moritz    Hermann,    on    local 

action,  182 
discovers    galvanoplastic    process, 

576      • 
his  boat  propelled  by  electricity, 

516 

on  electromagnet,  410 
Jar,  high  voltage,  64 
Leyden,  60 

Leyden,  capacity  of,  59,  314,  325 
„        cascade     arrangement    of, 

329 

discharge  of,  60,  330,  600 
discovery  of,  61 
energy  of  charge  of,  326 
seat  of  charge  of,  65 
spark  of,  339,  347 
theory  of,  314 
Jars,  Unit,  304 


INDEX 


697 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Jenkin,  Fleeming,  on  cable  as  con- 
denser, 321 

on  retardation  in  cables,  347 
Joints  in  magnetic  circuit,  406 
Jones,  John  Viriamu,  his  Lorenz  ap- 
paratus, 385 
Joule,  James  Prescott,  on  effects  of 

magnetization,  125 
evaluation  of  ohm,  385 
experiments    with   eddy    currents, 

500 

Law  of  heat  of  current,  459,  462 
limit  of  magnetization,  390 
magnetic  circuit,  403 
Mechanical  equivalent  of  heat,  459, 

567 

on  atmospheric  electricity,  358 
Joule  effect,  472 
Joule,  the,  381,  459 
Just,  tungsten  filaments  of,  481 

KAMERLINOH-ONNES,  H.,  discovery 

of  superconductors,  436 
Kapp,  Gisbert,  on  magnetic  circuit,  405 
Kathode,  178,  252 
Kathodic  "rays,"  344 
Ration,  255,  571 
Keeper,  103 
Kelvin,  Lord  (Sir  William  Thomson) , 

Electrometers,  80,  306 
Compass,  153 
Current  Balances,  427 
Electric  convection  of  heat  (Thom- 
son effect) ,  476 
Evaluation  of  ohm,  385 

"v,"  386 

Modified  Daniell's  cell,  198 
on  atmospheric  electricity,  358 
on  electric  images,  293 
Kelvin,  Lord,  on  electrostatics,  306 
on  length  of  spark,  333 
on  nomenclature  of  magnetic  poles, 

91  (footnote) 

on  sounds  in  condensers,  319 
predicts  electric  oscillations,  600 
proof  of  contact  electricity,  80 
Quadrant  Electrometer,  307 
Replenisher  (or  Mouse  Mill),  49, 

306,  307 

Thermo-electric  diagram,  476 
Water-dropping  Collector,  359 
Kerr,    Dr.    John,    Electro-optic    dis- 
coveries, 612 
Magneto-optic     discoveries,      126, 

393,  614 

Kerr's  effect,  614 
Kilowatt,  the,  381,  454 
Kirchhoff,  Gustav,  Laws  of  branched 
Circuits,  441 


Kite,  the  electric,  353 

Kohlrausch,    Friedrich,    on    residual 

charge,  319 

on  evaluation  of  ohm,  385 
Kundt,  August,  his  effect,  615 
Kuzel,  tungsten  filament  of,  481 

LAG  and  lead,  524 
Lagging  of  magnetization,  395 
Lamellar  magnetization,  120 
Laminated  magnets,  104 
Lamination  of  cores,  500,  508,  533, 

538 

Lamps,  arc,  486 

Lamps,  incandescent,  481,  482,  483 
Langley's,  S.  P.,  his  bolometer,  436 
Law,  cell,  188 
Laws  of  electrolysis,  569 

of  inverse  squares,    19,    131,    151, 
278,  288 

of    electro-magnetic    system,    217, 

409 
Lead,  used  in  accumulators,  572 

no  Thomson-effect  in,  476 
Lead  and  lag,  in  phase,  524 
Lead  of  brushes,  508 
Leakage,  magnetic,  405 

photoelectric,  619 

rate  of  electric,  350 
Le  Baillif,  diamagnetism,  398 
Leclanche,  Georges,  his  cell,  192 
Lemonnier,     discovers     atmospheric 

electricity,  358 

Lenard,    Philipp,    aluminium    "win- 
dow," 344 

Length  of  spark,  333 
Lenz  on  electromagnet,  410 
Lenz's  Law,  499 
Leyden  jar,  60 

prevention  of  piercing  spark,  63 

oscillatory  discharge  of,  600 

resonance  between  two,  602 

seat  of  charge  in,  65 
Leydens  (see  Condensers') 
Lichtenberg's  figures,  348 
Life  of  Lamps,  483 
Lifting-power  of  magnets,  116,  117 

of  electromagnets,  415 
Light  affects  resistance,  617 

affects  a  magnet,  611 

Electric,  481 

Electromagnetic  theory  of,  1,  609 

polarized,  rotated  by  magnet,  126, 
613,  614,  615 

velocity  of,  386,  609 
Lightning,  12,  353,  355 

Arresters,  561 

conductors,  35,  356 

duration  of,  347,  355 


698 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Lightning,  best  methods  of  protection 

from,  356 
Limit   of  heating  of  electromagnet, 

417 

magnetization,  390 
Lindsay,  James  Bowman,  telegraphy 

without  wires,  629 
Line-integral,  368  (footnote) 
Lines-of-force,  electric,  14,  17,  20,  22, 

24,  286 

magnetic,  99,  121,  362 
Lippmann,  G,,   Capillary   Electrom- 
eter, 269,  312 
Liquid  condensers,  572 
Liquids  as  conductors,  250,  569,  609 

resistance  of,  435,  436 
"Local  Action"  in  batteries,  186 
Locomotion,  electric,  562 
Locomotive  Electric,  564 
Lodestone,  85 

Lodge,  Sir  Oliver,  on  resonance,  602 
arrangements  of  oscillatory  circuits, 

600 

his  detector  or  coherer,  606 
his  oscillator,  607 
his  valve,  634 
on  oscillatory  nature  of  lightning, 

356,  607 

Lodge,  Sir  Oliver,  transmission  of  wire- 
less signals,  620 
Lohys,  391 

"Long"  and  "short"  coils  for  mag- 
nets, 417 

Long  and  short  coil  instruments,  440 
Long  distance  transmission  of  energy, 

552 

Lorentz,  Hendrik  Antoon,  385 
Lorenz,  L.,   on  evaluation    of    ohm, 

385 

Loss  of  charge,  350,  619,  634 
Louis    XV.    electrifies    700    monks, 

270 

Lullin's  experiment,  335 
Luminous  effects  of  spark,  339 

MACHINE,  Electric,  43 

alternating  current,  534 

cylinder,  43 

dynamo-electric,  507 

Hotel's,  53 

hydro-electrical,  48 

influence,  49 

magneto-electric,  506 

plate,  44 

Toepler's  or  Voss,  51 

Wimshurst,  52 

Magne-crystallic  action,  401 
Magnet,  breaking  a,  93 

earliest  book  on,  87 


Magnetic  actions  of  current,  209,  367, 

420 

attraction  and  repulsion,  90, 123,420 
cage,  100 
circuit,  403 
creeping,  395 
field,  118,  215,  420 

„     rotatory,  548,  549 
fields,  superpostition  of,  144,  420 
figures,  121,  122,  123,  215,  420 

theory  of,  143 
flux,  363,  405 

,,     density,  390  (footnote) 
forco,  95,  362  (a) 

,,       measurement  of,  132 
hysteresis,  394,  395,  510 
induction,  99,  390  (footnote) 
iron-ore,  85 
lag,  alleged,  395 
leakage,  405 
lines-of-force,    99,    121,    122,    123, 

376,  389,  400,  405,  420,  510 
field  due  to  current,  215,  420 
maps,  161 
meridian,  157 
metals,  97,  389,  396 
model  (Swing's),  129 
moment,  137,  373,  388 
needle,  89,  152 

oxide  of  iron,  85,  191  (footnote) 
paradox,  a,  145 

permeability,  99,  390,  393,  609 
pole,  unit,  142,  379 
poles,  neutralizing  action  of,  145 
potential,  362,  374,  375 
proof-plane,  249 
saturation,  115,  390 

Beetz,  on,  127 
screen,  100 
separators,  397 
shell,  120,  216,  363  (h),  375 

„     force  due  to,  372 

,,     potential  due  to,  375 
shunts,  408 
steels,  396 
storms,  166,  361 
substances,  96,  389,  396 
susceptibility,  392 
units,  379 
writing,  124 
Magnetism,  85 

action  of,  on  light,  126,  127 
destruction  of,  112 
distribution  of,  119 
lamellar,  120 
laws  of,  91,  130,  362 
of  gases,  398,  402 
permanent,  101 
phenomenon  of  rotation,  613 


INDEX 


699 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Magnetism,  residual,  115,  391 

solenoidal,  120,  374 

temporary,  101,  115 

terrestrial,  94,  156 

theories  of,  102,  127,  613 

unit  of,  142,  379 
Magnetite  (magnetic  ore),  85 

Arc  lamp,  493 
Magnetization,  anomalous,  401 

coefficient  of  (see  Susceptibility) 

cycles  of,  394,  395 

intensity  of,  392 

lamellar,  120 

mechanical  effects  of,  125 

methods  of,  105-110 

solenoidal,  120,  374 
Magnetization,  sound  of,  125,  593 

time  needed  for,  419 
Magneto-electric  machines,  506 
Magneto-electricity,  83,  239,  506 
Magnetographs,  167 
Magnetometer,  140 

Kew  pattern,  103 

self-registering,  167 
Magnetomotive-force,  368,  403 
Magneto-optic  Rotations,  613 
Magnets  (see  also  Electromagnet) 

action  of,  on  the  arc,  494 

action  of  light  on,  611 

artificial,  86 

compound,  104 

forms  of,  103 

lamellar,  120 

laminated,  104,  533 

methods  of  making,  105-110 

natural,  85,  103 

natural  and  artificial,  85,  86 

permanent,  103 

,,  pull  of,  at  a  distance, 

146 

physiological  action  of,  275 

power  of,  117 

unvarying,  113 

Mance,  Sir  Henry,  his  method,  449 
Manganese  steel,  396 
Manganin,  436 
Maps,  magnetic,  161 
Marconi,   Guglielmo,   transmission  of 

signals  by  waves,  620 
Mariner's  Compass,  152 
Marked  pole,  90 

Mascart,  E.,  on  atmospheric  electri- 
city, 360 

Matteucci,    Carlo,    on    physiological 
effects,  77,  272 

on  electromotive-force  in  muscle, 

273 

Maxwell,  James  Clerk,  Electro-mag- 
netic theory  of  light,  429,  609 


Law  of  alternating  currents,  526 

Law    of    electromagnetic    system, 
217,  376,  409 

measurement  of  "v, "  386 

on  Electric  Images,  293 

on  protection  from  lightning,  35, 
356 

on  residual  charge  of  jar,  319 

rule  for  action  of  current  on  mag- 
net, 217,  376 

Theorem   of   equivalent   magnetic 
shell,  378 

Theory  of  Magnetism,  127 
Measurement  of  capacity,  451 

of  currents,  238,  425,  427,  444 

of  E.M.F.,  448 

of  internal  resistance,  449 

of  magnetic  forces,  132 

of  mutual  inductance,  497 

of  permeability,  393 

of  power,  457 

of  resistance,  443,  445 

of  self-inductance,  452,  501,  502 
Mechanical  depolarization,  188 

effects  of  discharge,  47,  335 
,,      of  magnetization,  125 
,,   *  in  dielectric,  319,  612 
Medical  Applications  of  Electricity, 

274 
Medium,  action  in,  6,  4,  297 

elasticity  and  density  of,  387 

energy  paths  in,  610 

velocity  of  waves  in,  386,  609 
Mega-,  381 
Megohm,  381 
Meidinger's  cell,  198 
Melloni,  Macedonia,  his  thermopile, 

477 

Meridian,  Magnetic,  157 
Metallic  glow-lamps,  483 
Metals,    electro-chemical    power    of, 
568 

electrodeposition  of,  575 

refining  by  electricity,  575 
Meter  Bridge,  447 
Meters,  460 

Metric  system,  the,  298 
Mho,  the,  434 
Mica,  inductivity  of,  317 
Micro-,  381 
Microfarad,  the,  301,  381 

condenser,  323 
Microphone,  the,  595 
Milli-,  381 
Milli-ampere,  381 
Mines,  electric,  fuses  for  firing,  316, 

432 

Minolta's  cell,  198 
Mirror  Galvanometer,  228 


700 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Molecular  action  of  magnetism,  127 

actions  of  current,  265 

theory  of  Electric  action,  8 
Moment  of  circular  coil,  373 

of  inertia,  388 

magnetic,  137,  388 
Moment  of  Couple,  138 
Morse,  Samuel  F.  B.,  his  Telegraph 
instrument,  582  a 

telegraphy  without  wires,  629' 
Morse  Alphabet,  the,  582  b 
Moscicki's  condenser,  63 
Motion,  law  of,  in  magnetic  field,  217, 

409 

Motor-generators,  544,  545 
Motors,  516 

alternating,  547 

excitation  and  speed  of,  521 

induction,  549 

synchronous,  484 
Mouse-mill  (see  Replenisher) 
Miiller,  Johannes,  on  strength  of  elec- 
tromagnets, 410 
Multicellular  voltmeter,  309 
Multiplier,  Schweigger's,  213 
Multipolar  dynamos,  509 
Muscular  contractions,  271,  272 
Musschenbroek,  Peter  Van,  discovery 

of  Ley  den  jar,  61 
Mutual  inductance,  497 

inductance,  coefficient  of,  378 

potential,  378 

NAPOLEON  Ill's  cell,  202 
Navigation,  electric,  516 
Needle,  magnetic,  89 

telegraph,  581 

Negative  electrification,  6,  351 
Nernst  lamps,  485 
Neutralizing  brush,  50 
Newton,  Sir  Isaac,  his  lodestone,  117 
suggests  electric  origin  of  lightning, 

12,  353 
suggests  glass  for  electric  machines, 

42 
Niagara  Falls,  transmission  of  power 

from,  552 
Nickel,  97,  396 
Nipher,  Francis  E.,  brush  discharge, 

348 
Nitrates  from  air,  production  of,  336, 

463 

Nitrogen-filled  lamps,  484 
Nobili,   Leopoldo,   on  muscular   con- 
tractions, 77 
on   currents  of   animal  electricity, 

273 

discovers  Nobili's  rings,  569 
Nodon,  electric  valve,  569 


Noe  thermopile,  477 
Non-conductors,  11,  437 
Non-electrics,  4 
North  and  south,  91,  156 

magnetic  pole,  the,  91,  156 
Null  methods,  223,  308,  443  (c),  445, 
448  (6),  449  (e),  451  (d) 

OBLIQUE  currents,  laws  of,  421 
Oersted,    Hans    Christian,    discovers 
magnetic  action  of  current,  209, 
215 

Ohm,  Dr.  Georg  Simon,  206 
"Ohm's  Law,"  206,  431 
Ohm,  the,  381,  and  Appendix  B 

evaluation  of,  385 
Ohmmeter,  453 
Oil,  dielectric  strength,  of,  335 
One-fluid  theory  of  electricity,  8 
Opposition  method,  449 
Optical  strain,  electrostatic,  612 
rotation,  electromagnetic,  613,  614, 

615 
Oscillating       arc       radio-telegraphic 

transmitter,  624 
Oscillation-transformer,  603 
Oscillations,  electric,  356,  600 
method  of,  223 
method  of  (for  electrostatics),   135 

(footnote) 

method  of  (for  magnetic  measure- 
ment), 135,  136,  388 
Oscillator,  605,  607 
Oscillograph,  236 
Osmose,  electric,  266 
Other  sources  of  electrification  than 

friction,  13,  17 
Output  of  dynamo,  510 
Over-compounding,  513 
Overhead  line  for  tramcars,  563 
Oxygen  magnetic,  398 
Ozone,  253,  336,  353  (footnote) 

PACINOTTI'S  armature,  508 

Page,  Charles  G.,  discovers  magnetic 

sounds,  125 
Parallel,  capacities  in,  328 

cells  in,  176,  438 

circuits,  laws  of,  421 

lamps  in,  558 

resistances  in,  441 

running  of  alternators,  537 
Paramagnetic  bodies,  398,  399 
"Passive"  state  of  iron,  191 
Pathological  dose  of  current,  274 
Peace,  on  length  of  spark,  333 
Peltier,    Athanase,    his    electrometer, 
305,  359 

heating  effect  at  junctions,  472 


INDEX 


701 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Penetrative  power  of  discharge,  335 
Peregrinus,  Peter,  book  on  the  mag- 
net, 87 

Periodic  current,  522 
Periodicity  (see  Frequency) 

of  aurora  and  magnetic  storms,  165, 

166,  361 

Permanent  magnets,  103 
Permeability,  99,  390,  609 

measurement  of,  393 
Permeance,  404 

Perrin,  Jean,  on  kathode  rays,  344 
Perry,  John,  his  meter,  460 
Persistence  (see  Time-constant) 
Phase,  522,  524 
Phosphorescence  caused  by  discharge, 

342,  343 

Photo-chemical  excitation,  618 
Photographic  plate  affected  by  dis- 
charge, 348 
Photophone,  617 
Photo-electric  property  of  selenium, 

617 

Physiological  actions,  270,  349 
Piercing  glass,  prevention  of,  63 
Piezo-electricity,  76 
Pinch  effect,  424 
Plane,  the  proof-,  32 

,,  for  magnetism,  249 

Plante,  Gaston,  secondary  cells,  572 
Plants,  electricity  of,  78,  272 
Plate  condenser,  57,  315,  325 

electrical  machine,  44 
Platinoid,  436 
Plucker,    Julius,    on    diamagnetism, 

etc.,  401 

Plunger  electromagnet,  416 
Poggendorff,  J.  C.,  his  cell,  189 
Points,  density  of  charge  on,  38,  292 

discharge   at,  43,  45,  46,  47,  292, 

353 

Poisson,  magne-crystallic  action,  401 
Polarity,  diamagnetic,  398 

magnetic,  92,  93,  127 
Polarization  (electrolytic)  in  battery 
cells,  183,  566 

of  Voltameter,  566,  572 

remedies  for,  185 

rotation  of  plane  of,  613  et  seq. 
Polarized  mechanism,  418 

relay,  584 
Poles  of  magnets,  88,  136 

of  pyroelectric  crystals,  75 

of  voltaic  battery,  176 
Polyphase  currents,  548 
Porous  cell,  196 
Porrefs  phenomenon,  266 
Portable  electrometer,  306  ' 
Portative  force,  117 


Post-Office  Bridge,  447 

relay,  584 
Positive  and  negative  electrification, 

6,  351 
Potential,  electric,  41,  280 

zero,  41,  282 

galvanometers,  237 

of  conducting  sphere,  287 

magnetic,  362,  374,  375 

,,         due  to  current,  377 

mutual,  of  two  circuits,  378 
Potential-divider  null  method,  451 
Potentiometer,  448 
Poulsen,  system,  622 
Powdered  metals,  conduction  of,  432 

sensitiveness  to  sparks,  606 
Powders,  electroscopic,  31,  47,  319, 

348 
Power,  454 

transmission  of,  551 
Power-factor,  531 
Power-houses,  554 
Power-stations,  554 
Poynting,   John  Henry,   on    energy- 
paths,  610 
Practical  units,  381 
Pressure  produces  electrification,  74 

effect  on  electrolysis,  569 

(voltage),  177 

Priestley,  Joseph,  on  electric  expan- 
sion, 320 

on  influence,  26  (footnote) 
Prime  conductor,  43 
Printing  telegraphs,  580 
Projector  arc  lamps,  490 
Proof-plane,  32 

magnetic,  249 

Protective  devices  for  electrical  cir- 
cuits, 561 

Protoplasm,  electric  property  of,  272 
Pyroelectricity,  75 
Pyrometer,  436,  480 
Pyrrhotine,   magnetic   properties  of, 
401 

QUADRANT  electrometer  (Lord  Kel- 
vin's), 307 

Quadruplex  telegraphy,  586 

"Quantity"  arrangement  of  cells, 
etc.,  207,  439 

Quantity  of  electricity,  unit  of,  21, 
279,  381 

Quartz  fibre,  319 

Quartz,  no  residual  charge  from,  319 
as  insulator,  30,  319 

Quenched  spark  radio-telegraphy, 
624 

Quetelet,  E.,  on  atmospheric  electric- 
ity, 358,  360 


702 


.  ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Quincke,   Georg,   on   diaphragm   cur- 
rents, 268 

on  electric  expansion,  320 
on  electro-optic  phenomena,  612 

Quinine,  use  of,  for  mapping  fields,  319 

RADIANT  state  of  matter,  344 
Radio-activity,  638 
Radio-micrometer,  478 
Radio-telegraphic  receivers,  625 

transmitters,  621 
Railways,  electric,  564. 
Rate  of  change  of  current,  497,  524 

(footnote) 

Ratio  of  electric  charge  to  mass,  639 
Ratio    of    electrostatic    to    electro- 
magnet units,  301,  386 
Ray,  electric  (torpedo),  77 
Rays,  canal,  344 

kathode,  344 
Rayleigh,  Lord,  current  balance,  427 

determination  of  ohm,  385 
Reactance,  526 

due  to  capacity,  528 
Recalescence,  114 
Reciprocal  accumulation,  49 
Recording  instruments,  167,  359,  554 
Redistribution  of  charge,  40 
Reduction  of  metals,  575 
Reflecting  galvanometer,  228 
Reflexion  of  electric  waves,  605 
Refractive  index,  609 
Registering  magnetographs  and  elec- 
trometers, 167,  359 
Reis,  Philipp,  invention  of  telephone, 

593 

Relays,  584 
Reluctance,  403 
Reluctivity,  403  (footnote) 
Remanence,  394 
Replenishes  49,  306,  307 
Repulsion  and  attraction  of  electri- 
fied bodies,  3,  5,  22,  24,  75,  279 
and  attraction,  experiments  on,  47 
and    attraction    of    currents,    365, 

420,  425 

and  attraction  of  magnets,  85,  90 
Repulsion  electrometers,  305 
Residual  charge  of  Leyden  jar,  62,  319 
„  „     of  cable,  321 

„  „      of  Voltameter,  572 

magnetism,  115,  129,  394 
Resinous  electricity,  6 
Resistance  and  heat,  461 
Resistance,  30,  179,  432,  461 
affected  by  temperature,  436 

light,  617 

„  magnetism,  429 

sound,  595 


Resistance,  as  a  velocity,  384 

bridge  or  balance,  445 

coils,  446 

internal,  of  cell,  205,  207,  439,  449 
,,  ,,      measurement     of, 

449 

laws  of,  432 

magnetic,  403 

measurement  of,  443  et  seq. 

of  gases,  179,  345 

of  glow-lamps,  482 

of  human  body,  271 

of  liquids,  179,  435 

specific,  433,  435 

to  alternating  currents,  532 

units  of,  379  et  seq. 
Resistivity,  433,  435 
Resonance,  529 
Resonating  circuits,  602 
Resonator,  605 

Resultant  magnetic  force,  118 
Retardation     of     currents     through 

cables,  321,  347,  588 
Retentivity  (magnetic),  101,  394 
Return  shock  or  stroke,  29,  355 
Reversal  of  influence  machines,  53 
Reversibility  of  processes  in   circuit, 

264,  455,  581 

Reversing-switch,  208,  248 
Reymond,  Du  Bois,  his  galvanometer, 
273 

on  animal  electricity,  273 

unpolarizable  electrodes,  273 
Rheostats,  432 
Riess,  Peter,  on  electric  distribution, 

39 

Righi,  Augusto,  spark  gap,  607 
Ritchie,  magnetic  circuit,  403 

his  motor,  516 

Hitter,  Johann  Wilhelm,  on  action  of 
current  on  sight,  270 

his  secondary  pile,  572 

on  subjective  galvanic  sounds,  270 

on  the  sensitive  plant,  272 
Roentgen,  Wilhelm  Conrad,  his  X-rays, 

352 

Rolling  friction,  13 
Romagnpsi,  Dr.,  discovers  magnetic 

action  of  current,  209 
Romas,  De,  his  electric  kite,  353 
Ronalds,  Sir  Francis,  invented  a  tele- 
graph, 580 

Rotation  of  plane  of  polarization,  613 
Rotations,  electromagnetic,  428 

Arago's,  500 
Rotatory  converters,  546 

magnetic  field,  548 
Roughness  of  surface  as  depolarizer, 
188 


INDEX 


703 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Rowland,  Henry  A.,  on  electric  con- 
vection, 429 

on  magnetic  circuit,  403 
Rubens,  his  thermopile,  477 
Riicker,     Sir^     Arthur     William,     on 
rationalization     of     dimensions, 
387 
Riicker  and  Thorpe,  magnetic  survey, 

161 

Ruhmkorff's  electromagnet,  398 
induction  coil,  246 
coil,  mutual  induction  of,  497 
Rutherford,   Sir  Ernest,   detection  of 

electric  waves,  620 
on  radio-activity,  638 

ST.  ELMO'S  FIRE,  353  (footnote) 
Safety-fuses,  337,  464,  467 
Salts,  electrolysis  of,  254,  569 
Sanderson,  J.  Burdon,  on  electric  sen- 
sitiveness of  carnivorous  plants, 
272 

Saturation,  magnetic,  115,  390  et  seq. 
Sawdust  battery,  171 
Scalar  quantities,  303 
Schuster,   Arthur,   on   electrolysis   of 

gases,  346 

Schweigger's  multiplier,  213 
Screening,  magnetic,  100 

inductive,  597 

Screening  of  eddy-currents,  500,  597 
Secohm,  502 

Secondary  actions  in  electrolysis,  569 
Secondary  batteries,  572 
Secular  variations  of  magnetic  ele- 
ments, 162 

Seebeck,  Thomas  Johann,  effect,  471 
Selenium,    photo-electric    properties 
of,  617 

resistance  of,  436  (table),  617 
Self-exciting  influence  machine,  50 

dynamo,  507 
Self-inductance,  501,  524 

in  electric  discharge,  600 

measurement  of,  502 
Self-recording  instruments,  167,  359, 

554 

Sending  and  receiving  in  radio-teleg- 
raphy, 627 

Sensitive  plant,  behaviour  of,  272 
Series,  arc  lamps  in,  487 

capacities  in,  329 

cells  in,  176,  438 

dynamos,  511 

resistances  in,  438 
Shackleton,  Sir  Ernest,  position  of  the 

S.  pole,  156 
Shadows,  electric,  47 

in  partial  vacuum,  343 


Sheet  conductor,   flow  of  electricity 

in,  442 
Shell,  magnetic,  120,  216,  377 

potential  due  to,  375 
Shielding,  magnetic,  100 
Shock,  electric,  270,  349 
Shunt,  230,  441 

coil  in  arc  lamps,  489 

dynamo,  511 

for  galvanometer,  230 

magnetic,  408 
Shuttle  armature,  506 
Siemens,    Alexander,    on    length    of 

spark,  333 
Siemens,  Werner,  on  dynamos,  506 

mercury  unit,  385 

electrodynamometer,  426 

shuttle-wound  armature,  506 

heating  in  Ley  den  jar,  319 
Siemens,  unit  of  conductance,  381 
Sight  affected  by  current,  270 
Silurus,  the,  77 
Sine  galvanometer,  227 
Sine  law,  522 
Singing  Arc,  495 
Single- needle  instrument,  581 
Single  touch,  105 
Siphon  recorder,  589 
Skew-symmetry  of  crystals,  75 
Skin  effect,  532 
Skin,  E.M.F.  in  the,  273 
Smee,  Alfred,  his  Battery,  188 
Smith,  F.  E.,  on  value  of  the  ohm, 

385 

Smith,  Frederick  John,  effect  on  pho- 
tographic plate,  348 
Smith,  Willoughby,  on  selenium,  617 
Soap-bubble,  electrified,  5      » 
Sodium  by  electrolysis,  569 
Solenoid  arc  lamps,  489 
Solenoid,  414 

magnetizing  force  of,  368 
Solid  angles,  151  (Appendix  A) 
Solidification,  70 
Solids,  conduction  in,  635 
Sound  of  magnetization,  125,  593 
Sounder,  the,  582 
Sources  of  electricity,  13,  67 
Spark,  12,  46,  47,  331 

duration  of,  347 

extinction  of,  561,  603 

length  of,  48,  246,  333,  353 
Spark-gap,  600,  603,  624,  627 
Sparking  at  commutator,  508 

at  contacts,  338 
Specific  resistance,  434 

inductive  capacity,  25,  57,  315,  319 
Speed  of  motor,  518 

of  signalling,  321,  322,  347 


704 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Sphere,  distribution  of  charge  over, 
38,  293  et  seq. 

potential  of,  287,  289 

capacity  of,  289 
Spiral  shortens  itself,  421 
Square  root  of  mean  square,  523 
Stalloy  (iron-silicon  alloy),  391 
Standard  bells,  200,  201 

effect  of  temperature  on,  200,  201 

ohm,  385 
Standards,  381 
Starting  resistances,  520 
Steady  strain,  357 

Steel  for  permanent  magnets,  111,  113 
Steel  hardening,  111 
Steel,  properties  of,  389 
Steel-facing,  576 
Stewart,  Balfour,  on  magnetic  storms, 

165 

Stoney,  Johnstone,  on  electron,  630 
Storms,  magnetic,  166 
Straight  conductor,  force  near,  220, 

370 

Strain,  dielectric,  66,  319,  612 
Strength  of  current,  179,  205,  381 

of   current   in   magnetic   measure, 
219,  220,  380  et  seq. 

of  dielectric,  319,  331 

of  magnet  pole,  116,  379 

of  magnetic  shell,  376 
Stress,  electric,  14,  17,  20,  22,  23,  66, 
297,  319,  331,  612 

electric,  optical  effect  of,  612 

magnetic,  121,  367,  420 
Striae  in  vacuum  tubes,  342,  345 
String  galvanometer,  232 
Strutt,  Hon.  Robert  John,  333 
Sturgeon,     William,    electromagnets, 
411 

induction  coil,  246 

on  magnetic  circuit,  403 
Submarine  telegraphs,  587 
Substations,  556 
Sulphuretted  hydrogen,  iron  negative 

to  copper  in,  81 
Sulzer's  experiment,  270 
Supply  meters,  460 
Surface  contact,  13 
Surface-density  of  charge,  38,  291 

limit  of,  291      v 

of  magnetism,  136,  362 
Surgical  applications,  274 
Susceptibility,  392 
Suspended-coil  galvanometers,  229 
Swammerdam's  frog  experiment,  271 
Swan's  incandescent  lamp,  482 
Switches,  208,  388 

Symmer,  on  two  kinds  of  electrifica- 
tion, 6 


Synchronizing,  537 
Synchronous  converters,  546 
Syntony,  602 

TAIT,    PETER    GVTHRIE,    thermo- 
electric diagram,  476 
Tangent  galvanometer,  225 

of  angle  of  lag,  526 
Tapper,  581 

Taste  affected  by  current,  270 
Telegraph,  electric,  580 
Bain's  chemical,  262 
Morse's  instrument,  582  a 
Telegraph,  needle  instrument,  581 
Telegraphone,  599 
Telegraphy,  diplex,  586 
duplex,  586 
quadruplex,  586 
submarine,  587 

Telegraphy  without  wires,  629 
Telephone,  Philipp  Reis's,  593 
currents  of,  271 

Graham  Bell's  magneto-electric,  593 
Varley's  (condenser),  319,  593 
Exchanges,  596 
Temperature  affects  resistance,   199, 

436 

affected  by  resistance,  461 
effect  on  length  of  spark,  333,  334 
of  the  arc,  486 
Tempering  of  steel,  111 
Tension,  electric,  14,  17,  20,  22,  24, 
66,  291  (footnote),  297,  319,  331, 
612 
Terquem,  A.,  parrot-cage  experiment, 

34 

Terrestrial  Magnetism,  94,  156,  388 
Tesla,  Nikola,  high  frequency  appa- 
ratus of,  603 
Test  for  weak  currents   (chemical), 

262,  336 
for  weak  currents  (physiological), 

272 

Testing  for  faults,  585 
Tetanization  produced  by  interrupted 

currents,  272 

Theories  of  Electricity,  8,  351,  630 
Theories  of  Magnetism,  102,  127 
„       Ampere's,  430 
„       Swing's,  129 
„       Maxwell's,  127 
„       Weber's,  127,  129 
Theory    of    Electrolysis,    Grotthuss's 

and  Clausius's,  570 
Theory  of  Earth's  magnetiso,  168 

of  light,  609 
Thermal  cross,  479 
Thermo-electricity,  79,  471 
Thermo-electric  Diagram,  476 


INDEX 


705 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Thermo-electric  Pyrometers,  480 
Thermo-electromotive  Series,  474 
Thermo-galvanometer,  477 
Thermopile,  477 

Thompson,  Silvanus  Phillips,  on  mag- 
netic figures  due  to  currents,  215, 
420 

on  positive  and  negative  states,  351 

on  opacity  of  tourmaline,  609 

on  general  electromagnetic  law,  409 

on  radio-activity,  638 
Thomson,  Sir  Joseph  J.,  on  Contact 

Electricity,  82 

Thomson,  Sir  Joseph  J.,  experiments 
on  electrons,  639 

on  conductivity  of  gases,  346 
Thomson,   Sir    William    (see   Kelvin, 
Lord) 

effect,  476 

Thomson,  Elihu,  high  frequency  ap- 
paratus of,  603 

his  meter,  460 

on     alternating-current     magnets, 
533 

on  welding,  468 

repulsion  experiment  of,  533 
Thomson-Houston  dynamos,  514 
Thorpe  and  Rucker,  magnetic  survey, 

161 

Three-phase  currents,  535 
Three- wire  system,  559 
Thunder,  12,  355 
Thunderstorms,  353,  354 
Thury  system,  552 
Time-constant,  504 
Tinfoil  Condensers,  56,  322 
Tiv,oli,  transmission  of  power  from, 

552 

Toepler,  A.,  his  Influence  Machine,  51 
Tongs,  Discharging,  60 
Torpedo  (electric  fish),  77,  262 
Torque,  138 
Torque  of  motor,  518 
Torsion   affected   by   magnetization, 

125 

Torsion  Balance,  or      |  Coulomb's, 
Torsion  Electrometer,  J       18,  134 
Torsion  method,  222,  223 
Tourmaline,  75,  348,  609 
Tramways,  electric,  563 
Transformers,  245,  538,  540 

construction  of,  540 

coupling  of  circuits  by,  543 

for  vacuum  tubes,  342 

oscillation-,  603 

self  and  mutual  inductance  in,  542 
Transmission  of  power,  551,  552 
Trolley  wheel  for  tramcars,  563 
Tube  of  force,  363 (g) 

2z 


Tuning,  602,  620,  625 
Tuning-fork  method,  451 
Turbines,  steam,  554 

water,  551,  554 
Turbo-alternators,  536 
Two-fluid  cells,  196 
Two-fluid  theory,  8 
Two  kinds  of  Electrification,  6,  7 
Two  kinds  of  Magnetic  poles,  91 
Tyndall,  John,  diamagnetic  polarity, 
400 

magne-crystallic  action,  401 

ULTRA-GASEOUS  matter,  344 
Ultra-violet  waves,  333 

discharge  by,  619 
Unit,  Board  of  Trade,  558,  567 
Unit  jar,  304 

Units  and  standards,  Board  of  Trade 
(see  Appendix  E) 

electromagnetic,  379  et  seq. 

electrostatic,  301  et  seq. 

fundamental  and  derived,  298,  299 

ratio    of    electrostatic    to    electro- 
magnetic, 279  (footnote),  301,  386 
Unipolar  Machines,  515 
Unpolarizable  electrodes,  273 
Unvarying  magnets,  113 
Ure,  Dr.,  on  animal  electricity,  271 

"v,"  386,  609 

Vacuum,      induction      takes      place 
through,  66,  99,  100 

partial,  spark  in,  12,  342 

discharge   will   not   pass   through, 
333,  636 

tubes,  342,  343 
Valves,  electric,  432,  634 
Vapour  lamps,  496 
"Variation,"  the  (see  Declination) 
Variation  of  Declination  and  Dip  — 

annual  and  diurnal,  163 

geographical,  157,  161 

secular,  162 

of  electrification  of  the  atmosphere, 

360 

Varley,    Cromwell   Fleetwood,    on   ca- 
pacity of  polarization,  572 

telegraph,  580 
Varley,  Samuel  Alfred,  his  telephone, 

319,  593 

.    early  dynamo,  507 
Vector  quantities,  303 
Vegetables,  Electricity  of,  78 

carnivorous,  sensitiveness  of,  272 
Velocity  of  discharge,  347 

of  electric  waves,  609 

of  light,  386,  609 

resistance  as  a,  384 


706 


ELECTRICITY  AND  MAGNETISM 


The  Numbers  refer  to  the  Numbered  Paragraphs. 


Verdefs  constant,  613 
Vibrator  for  measuring  capacity,  451 
Villari,  Emilio,  effect  of  tension,  391 
Violet  waves  (see  Ultra-violet) 
Virtual  volts  and  virtual  amperes,  523 
Vitreous  electricity,  6 
Volt,  177,  381 

Volta,  Alessandro,  his  Electrophorus, 
26 

Condensing  Electroscope,  80 

Contact  Series,  81 

Crown  of  Cups,  173 

on  Atmospheric  Electricity,  359 

on  Contact  Electricity,  80,  171 

on  Electric  Expansion,  320 

on  Electrification  due  to  combus- 
tion, 71 

Subjective  Sounds  due  to  Current, 
270 

Yalta's  Law,  88,  171 

Voltaic  Pile,  172 

Voltage,  high  and  extra  high,  553 
Voltaic  Electricity  (see  Current  Elec- 
tricity) 

arc,  486 

battery,  174,  186 ;  pile,  172 

cell,  simple,  170 
Voltameter,  258,  259,  260,  566 
Voltmeter,  237 

Cardew's,  465 

electrostatic,  309 
Voltmeters,  hot  wire,  237 

electromagnetic,  237 

moving  coil,  237 
Voss  machine,  51 

WARBURG,  E.,  on  hysteresis,  395 
Water,  Electrolysis  of,  251,  566 
Water-dropping,  discharge  by,  359 
Watt,  the,  381,  454 
Wattmeter,  458 
Watts,  true  and  apparent,  531 
Wave  trains,  620,  622 
Waves,  electric,  600 


Weber,    Wilhelm,    the    Electro-dyna- 
mometer, 425 

on  diamagnetic  polarity,  400 
evaluation  of  ohm,  385 
of  "v,"  386 

theory  of  magnetism,  127,  129 
Welding  by  electricity,  468 
Welsbach,  Auer  von,  electric  lamps  of, 

481 
Weston,  Edward,  voltmeter,  237 

standard  cell,  201 
Wheatstone,  Sir  Charles,  on  the  brush 

discharge,  340 
Automatic  Telegraph,  580 
Dynamo-electric  Machines,  507 
on  supposed  velocity  of  electricity, 

347 

Wheatstone 's  Bridge  or  Balance,  445 
Whirls,  magnetic,  215,  420 
Wilcke,   A.,  electrophorus,   26   (foot- 
note) 

Wilson,  C.  T.  R.,  experiments  on  con- 
duction in  gases,  633 
his  electrometer,  310 
Wimshurst,  James,  influence  machine, 

52 

Wind,  electric,  47,  348 
Winding    of   electromagnets,    403    et 
seq.,  414,  417  (and  see  page  669) 
Window,  aluminium,  344 
Wireless  telegraphy,  principles  of,  620 
Wireless  telephony,  628 
Wohler's  cell,  202 
Wollaston's  Battery,  188 
Work  by  conductor  cutting  lines,  366 

ZAMBON-I'S  Dry  Pile,  17,  203,  311 
Zanotti,   experiment  on  grasshopper, 

271 

Zeeman,  P.,  effect,  606 
Zero  Potential,  41,  282 
Zero  of  temperature,  resistance  near, 

436 
Zinc  as  fuel,  174 


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,    »\  '   " 


;  :'•...'•;•... -\ "="•  • 


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10m-7,'44(10G4s) 


RI36819 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


